diff --git a/packages/google-cloud-domains/setup.py b/packages/google-cloud-domains/setup.py
index 622896f640fc..247ae230ac36 100644
--- a/packages/google-cloud-domains/setup.py
+++ b/packages/google-cloud-domains/setup.py
@@ -46,7 +46,7 @@
         # NOTE: Maintainers, please do not require google-api-core>=2.x.x
         # Until this issue is closed
         # https://github.com/googleapis/google-cloud-python/issues/10566
-        "google-api-core[grpc] >= 1.28.0, <3.0.0dev",
+        "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
         "proto-plus >= 1.15.0",
     ),
     python_requires=">=3.6",
diff --git a/packages/google-cloud-domains/testing/constraints-3.6.txt b/packages/google-cloud-domains/testing/constraints-3.6.txt
index c77c3226f091..fe87928968f0 100644
--- a/packages/google-cloud-domains/testing/constraints-3.6.txt
+++ b/packages/google-cloud-domains/testing/constraints-3.6.txt
@@ -19,5 +19,5 @@
 #
 # 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==1.28.0
+google-api-core==1.31.5
 proto-plus==1.15.0