diff --git a/python/pyarrow/_compute.pyx b/python/pyarrow/_compute.pyx
index 1c0c779f603..9074946ffdd 100644
--- a/python/pyarrow/_compute.pyx
+++ b/python/pyarrow/_compute.pyx
@@ -1221,13 +1221,19 @@ class ReplaceSubstringOptions(_ReplaceSubstringOptions):
     replacement : str
         What to replace the pattern with.
     max_replacements : int or None, default None
-        The maximum number of strings to replace in each
-        input value (unlimited if None).
+        The maximum number of replacements to make in each
+        input value (unlimited if None or -1). If specified,
+        must be >= 0.
     """
 
     def __init__(self, pattern, replacement, *, max_replacements=None):
         if max_replacements is None:
             max_replacements = -1
+        if max_replacements < -1:
+            raise ValueError(
+                f"max_replacements must be >= -1, got {max_replacements}. "
+                "Use None or -1 for unlimited replacements."
+            )
         self._set_options(pattern, replacement, max_replacements)
 
 
diff --git a/python/pyarrow/tests/test_compute.py b/python/pyarrow/tests/test_compute.py
index d4d44e9347e..4f1e81616da 100644
--- a/python/pyarrow/tests/test_compute.py
+++ b/python/pyarrow/tests/test_compute.py
@@ -1244,6 +1244,30 @@ def test_replace_plain():
     assert ar.tolist() == ['barzfoo', 'bard', None]
 
 
+def test_replace_substring_negative_max_replacements():
+    # GH-39149: negative max_replacements should raise ValueError,
+    # not cause an indefinite hang.
+    with pytest.raises(ValueError, match="max_replacements must be >= -1"):
+        pc.ReplaceSubstringOptions(pattern='a', replacement='b',
+                                   max_replacements=-3)
+    with pytest.raises(ValueError, match="max_replacements must be >= -1"):
+        pc.ReplaceSubstringOptions(pattern='a', replacement='b',
+                                   max_replacements=-2)
+    # -1 and None are valid (unlimited)
+    opts = pc.ReplaceSubstringOptions(pattern='a', replacement='b',
+                                      max_replacements=-1)
+    assert opts.max_replacements == -1
+    opts = pc.ReplaceSubstringOptions(pattern='a', replacement='b')
+    assert opts.max_replacements == -1
+    # Non-negative values are valid
+    opts = pc.ReplaceSubstringOptions(pattern='a', replacement='b',
+                                      max_replacements=0)
+    assert opts.max_replacements == 0
+    opts = pc.ReplaceSubstringOptions(pattern='a', replacement='b',
+                                      max_replacements=5)
+    assert opts.max_replacements == 5
+
+
 def test_replace_regex():
     data = pa.array(['foo', 'mood', None])
     expected = ['f00', 'm00d', None]