diff --git a/git/index/fun.py b/git/index/fun.py
index 16ec744e2..59fa1be19 100644
--- a/git/index/fun.py
+++ b/git/index/fun.py
@@ -3,6 +3,7 @@
 # NOTE: Autodoc hates it if this is a docstring
 
 from io import BytesIO
+from pathlib import Path
 import os
 from stat import (
     S_IFDIR,
@@ -21,6 +22,7 @@
     force_text,
     force_bytes,
     is_posix,
+    is_win,
     safe_decode,
 )
 from git.exc import (
@@ -76,6 +78,10 @@ def hook_path(name: str, git_dir: PathLike) -> str:
     return osp.join(git_dir, 'hooks', name)
 
 
+def _has_file_extension(path):
+    return osp.splitext(path)[1]
+
+
 def run_commit_hook(name: str, index: 'IndexFile', *args: str) -> None:
     """Run the commit hook of the given name. Silently ignores hooks that do not exist.
     :param name: name of hook, like 'pre-commit'
@@ -89,8 +95,15 @@ def run_commit_hook(name: str, index: 'IndexFile', *args: str) -> None:
     env = os.environ.copy()
     env['GIT_INDEX_FILE'] = safe_decode(str(index.path))
     env['GIT_EDITOR'] = ':'
+    cmd = [hp]
     try:
-        cmd = subprocess.Popen([hp] + list(args),
+        if is_win and not _has_file_extension(hp):
+            # Windows only uses extensions to determine how to open files
+            # (doesn't understand shebangs). Try using bash to run the hook.
+            relative_hp = Path(hp).relative_to(index.repo.working_dir).as_posix()
+            cmd = ["bash.exe", relative_hp]
+        
+        cmd = subprocess.Popen(cmd + list(args),
                                env=env,
                                stdout=subprocess.PIPE,
                                stderr=subprocess.PIPE,
diff --git a/test/test_index.py b/test/test_index.py
index 02cb4e813..233a4c643 100644
--- a/test/test_index.py
+++ b/test/test_index.py
@@ -13,6 +13,7 @@
 )
 import tempfile
 from unittest import skipIf
+import shutil
 
 from git import (
     IndexFile,
@@ -52,8 +53,9 @@
 
 HOOKS_SHEBANG = "#!/usr/bin/env sh\n"
 
+is_win_without_bash = is_win and not shutil.which('bash.exe')
+
 
-@skipIf(HIDE_WINDOWS_KNOWN_ERRORS, "TODO: fix hooks execution on Windows: #703")
 def _make_hook(git_dir, name, content, make_exec=True):
     """A helper to create a hook"""
     hp = hook_path(name, git_dir)
@@ -881,7 +883,7 @@ def test_pre_commit_hook_fail(self, rw_repo):
         try:
             index.commit("This should fail")
         except HookExecutionError as err:
-            if is_win:
+            if is_win_without_bash:
                 self.assertIsInstance(err.status, OSError)
                 self.assertEqual(err.command, [hp])
                 self.assertEqual(err.stdout, '')
@@ -896,6 +898,7 @@ def test_pre_commit_hook_fail(self, rw_repo):
         else:
             raise AssertionError("Should have caught a HookExecutionError")
 
+    @skipIf(HIDE_WINDOWS_KNOWN_ERRORS, "TODO: fix hooks execution on Windows: #703")
     @with_rw_repo('HEAD', bare=True)
     def test_commit_msg_hook_success(self, rw_repo):
         commit_message = "commit default head by Frèderic Çaufl€"
@@ -920,7 +923,7 @@ def test_commit_msg_hook_fail(self, rw_repo):
         try:
             index.commit("This should fail")
         except HookExecutionError as err:
-            if is_win:
+            if is_win_without_bash:
                 self.assertIsInstance(err.status, OSError)
                 self.assertEqual(err.command, [hp])
                 self.assertEqual(err.stdout, '')