diff --git a/python/pyarrow/array.pxi b/python/pyarrow/array.pxi
index b7f3a46f9e14..7748a743bbbb 100644
--- a/python/pyarrow/array.pxi
+++ b/python/pyarrow/array.pxi
@@ -2290,15 +2290,15 @@ cdef class Array(_PandasConvertible):
 
     def __add__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('add_checked', [self, other])
+        return _array_binop_or_notimplemented('add_checked', self, other)
 
     def __truediv__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('divide_checked', [self, other])
+        return _array_binop_or_notimplemented('divide_checked', self, other)
 
     def __mul__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('multiply_checked', [self, other])
+        return _array_binop_or_notimplemented('multiply_checked', self, other)
 
     def __neg__(self):
         self._assert_cpu()
@@ -2306,31 +2306,43 @@ cdef class Array(_PandasConvertible):
 
     def __pow__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('power_checked', [self, other])
+        return _array_binop_or_notimplemented('power_checked', self, other)
 
     def __sub__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('subtract_checked', [self, other])
+        return _array_binop_or_notimplemented('subtract_checked', self, other)
 
     def __and__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('bit_wise_and', [self, other])
+        return _array_binop_or_notimplemented('bit_wise_and', self, other)
 
     def __or__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('bit_wise_or', [self, other])
+        return _array_binop_or_notimplemented('bit_wise_or', self, other)
 
     def __xor__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('bit_wise_xor', [self, other])
+        return _array_binop_or_notimplemented('bit_wise_xor', self, other)
 
     def __lshift__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('shift_left_checked', [self, other])
+        return _array_binop_or_notimplemented('shift_left_checked', self, other)
 
     def __rshift__(self, object other):
         self._assert_cpu()
-        return _pc().call_function('shift_right_checked', [self, other])
+        return _array_binop_or_notimplemented('shift_right_checked', self, other)
+
+
+def _array_binop_or_notimplemented(op_name, left, right):
+    # Same NotImplemented fallback as Scalar.__add__ et al, see GH-49826.
+    # Only swallow TypeError for genuinely foreign types; propagate when
+    # the right operand is already Arrow-native so type errors are visible.
+    try:
+        return _pc().call_function(op_name, [left, right])
+    except TypeError as e:
+        if isinstance(right, (Scalar, Array)):
+            raise
+        return NotImplemented
 
 
 cdef _array_like_to_pandas(obj, options, types_mapper):
diff --git a/python/pyarrow/scalar.pxi b/python/pyarrow/scalar.pxi
index a6377b2bb707..a22bbbaa3e0e 100644
--- a/python/pyarrow/scalar.pxi
+++ b/python/pyarrow/scalar.pxi
@@ -199,37 +199,55 @@ cdef class Scalar(_Weakrefable):
         return _pc().call_function('abs_checked', [self])
 
     def __add__(self, object other):
-        return _pc().call_function('add_checked', [self, other])
+        return _binop_or_notimplemented('add_checked', self, other)
 
     def __truediv__(self, object other):
-        return _pc().call_function('divide_checked', [self, other])
+        return _binop_or_notimplemented('divide_checked', self, other)
 
     def __mul__(self, object other):
-        return _pc().call_function('multiply_checked', [self, other])
+        return _binop_or_notimplemented('multiply_checked', self, other)
 
     def __neg__(self):
         return _pc().call_function('negate_checked', [self])
 
     def __pow__(self, object other):
-        return _pc().call_function('power_checked', [self, other])
+        return _binop_or_notimplemented('power_checked', self, other)
 
     def __sub__(self, object other):
-        return _pc().call_function('subtract_checked', [self, other])
+        return _binop_or_notimplemented('subtract_checked', self, other)
 
     def __and__(self, object other):
-        return _pc().call_function('bit_wise_and', [self, other])
+        return _binop_or_notimplemented('bit_wise_and', self, other)
 
     def __or__(self, object other):
-        return _pc().call_function('bit_wise_or', [self, other])
+        return _binop_or_notimplemented('bit_wise_or', self, other)
 
     def __xor__(self, object other):
-        return _pc().call_function('bit_wise_xor', [self, other])
+        return _binop_or_notimplemented('bit_wise_xor', self, other)
 
     def __lshift__(self, object other):
-        return _pc().call_function('shift_left_checked', [self, other])
+        return _binop_or_notimplemented('shift_left_checked', self, other)
 
     def __rshift__(self, object other):
-        return _pc().call_function('shift_right_checked', [self, other])
+        return _binop_or_notimplemented('shift_right_checked', self, other)
+
+
+def _binop_or_notimplemented(op_name, left, right):
+    # Scalar arithmetic dunders must return NotImplemented for argument types
+    # pyarrow.compute does not recognize so Python's reflected-operator
+    # fallback (__radd__ etc.) kicks in on user-defined classes.
+    # See GH-49826.
+    #
+    # Only swallow TypeError for genuinely foreign types (non-Arrow).  If
+    # the right operand is already an Arrow Scalar or Array, any TypeError
+    # from call_function (e.g. mismatched Arrow types) should propagate so
+    # the caller sees a meaningful error rather than a silent NotImplemented.
+    try:
+        return _pc().call_function(op_name, [left, right])
+    except TypeError as e:
+        if isinstance(right, (Scalar, Array)):
+            raise
+        return NotImplemented
 
 
 _NULL = NA = None
diff --git a/python/pyarrow/tests/test_array.py b/python/pyarrow/tests/test_array.py
index a103519dc5ac..b27bce5945d9 100644
--- a/python/pyarrow/tests/test_array.py
+++ b/python/pyarrow/tests/test_array.py
@@ -4401,6 +4401,16 @@ def test_non_cpu_array():
         arr.validate(full=True)
 
 
+def test_array_radd_unknown_operand():
+    # GH-49826: Array.__add__ on an unknown right operand must return
+    # NotImplemented so Python falls back to right.__radd__.
+    class WithRadd:
+        def __radd__(self, other):
+            return "radd-called"
+
+    assert pa.array([1, 2]) + WithRadd() == "radd-called"
+
+
 def test_arithmetic_dunders():
     # GH-32007
     arr1 = pa.array([-1.1, 2.2, -3.3])
diff --git a/python/pyarrow/tests/test_scalars.py b/python/pyarrow/tests/test_scalars.py
index 08f9fcd55ce0..0456e8397658 100644
--- a/python/pyarrow/tests/test_scalars.py
+++ b/python/pyarrow/tests/test_scalars.py
@@ -1022,6 +1022,16 @@ def test_bitwise_dunders():
     assert (scl2 >> scl1).equals(pc.shift_right_checked(scl2, scl1))
 
 
+def test_scalar_radd_unknown_operand():
+    # GH-49826: Scalar.__add__ on an unknown right operand must return
+    # NotImplemented so Python falls back to right.__radd__.
+    class WithRadd:
+        def __radd__(self, other):
+            return "radd-called"
+
+    assert pa.scalar(1) + WithRadd() == "radd-called"
+
+
 def test_dunders_unmatching_types():
     # GH-32007
     error_match = r"Function '\w+' has no kernel matching input types"