diff --git a/.builders/scripts/repair_wheels.py b/.builders/scripts/repair_wheels.py
index 2168053b3afdf..bae851cc2d895 100644
--- a/.builders/scripts/repair_wheels.py
+++ b/.builders/scripts/repair_wheels.py
@@ -16,6 +16,9 @@
 import urllib3
 from utils import extract_metadata, normalize_project_name
 
+# Packages for which we're skipping the openssl-3 build check
+OPENSSL_PACKAGE_BYPASS = ["psycopg"]
+
 
 @cache
 def get_wheel_hashes(project) -> dict[str, str]:
@@ -97,6 +100,28 @@ def __str__(self):
         ]) + '.whl'
 
 
+def check_unacceptable_files(
+    wheel: Path,
+    bypass_prefixes: list[str],
+    invalid_file_patterns: list[str],
+):
+    """Check if a wheel contains any unacceptable files and exit if found."""
+    if any(wheel.name.startswith(pkg_prefix) for pkg_prefix in bypass_prefixes):
+        print(
+            f'Warning: Bypassing unacceptable file check for {wheel.name}'
+        )
+        return
+
+    unacceptable_files = find_patterns_in_wheel(wheel, invalid_file_patterns)
+    if unacceptable_files:
+        print(
+            f"Found copies of unacceptable files in external wheel '{wheel.name}'",
+            f'(matching {invalid_file_patterns}): ',
+            unacceptable_files,
+        )
+        sys.exit(1)
+
+
 def repair_linux(source_dir: str, built_dir: str, external_dir: str) -> None:
     from auditwheel.patcher import Patchelf
     from auditwheel.policy import WheelPolicies
@@ -129,15 +154,11 @@ def repair_linux(source_dir: str, built_dir: str, external_dir: str) -> None:
         if not wheel_was_built(wheel):
             print('Using existing wheel')
 
-            unacceptable_files = find_patterns_in_wheel(wheel, external_invalid_file_patterns)
-            if unacceptable_files:
-                print(
-                    f"Found copies of unacceptable files in external wheel '{wheel.name}'",
-                    f'(matching {external_invalid_file_patterns}): ',
-                    unacceptable_files,
-                )
-                sys.exit(1)
-
+            check_unacceptable_files(
+                wheel,
+                bypass_prefixes=OPENSSL_PACKAGE_BYPASS,
+                invalid_file_patterns=external_invalid_file_patterns,
+            )
             shutil.move(wheel, external_dir)
             continue
 
@@ -179,15 +200,11 @@ def repair_windows(source_dir: str, built_dir: str, external_dir: str) -> None:
         if not wheel_was_built(wheel):
             print('Using existing wheel')
 
-            unacceptable_files = find_patterns_in_wheel(wheel, external_invalid_file_patterns)
-            if unacceptable_files:
-                print(
-                    f"Found copies of unacceptable files in external wheel '{wheel.name}'",
-                    f'(matching {external_invalid_file_patterns}): ',
-                    unacceptable_files,
-                )
-                sys.exit(1)
-
+            check_unacceptable_files(
+                wheel,
+                bypass_prefixes=OPENSSL_PACKAGE_BYPASS,
+                invalid_file_patterns=external_invalid_file_patterns,
+            )
             shutil.move(wheel, external_dir)
             continue