diff --git a/packages/google-cloud-secret-manager/setup.py b/packages/google-cloud-secret-manager/setup.py
index 2cde04e1f0e0..b9c386d77eb8 100644
--- a/packages/google-cloud-secret-manager/setup.py
+++ b/packages/google-cloud-secret-manager/setup.py
@@ -24,7 +24,7 @@
 version = "2.11.1"
 release_status = "Development Status :: 5 - Production/Stable"
 dependencies = [
-    "google-api-core[grpc] >= 2.8.0, <3.0.0dev",
+    "google-api-core[grpc] >= 1.32.0, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*",
     "grpc-google-iam-v1 >= 0.12.4, <1.0.0dev",
     "proto-plus >= 1.15.0, <2.0.0dev",
     "protobuf >= 3.19.0, <4.0.0dev",
diff --git a/packages/google-cloud-secret-manager/testing/constraints-3.7.txt b/packages/google-cloud-secret-manager/testing/constraints-3.7.txt
index 18be4803cbc7..39a7c58e1e8c 100644
--- a/packages/google-cloud-secret-manager/testing/constraints-3.7.txt
+++ b/packages/google-cloud-secret-manager/testing/constraints-3.7.txt
@@ -5,7 +5,7 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-google-api-core==2.8.0
+google-api-core==1.32.0
 grpc-google-iam-v1==0.12.4
 proto-plus==1.15.0
 libcst==0.2.5