diff --git a/packages/google-cloud-dlp/setup.py b/packages/google-cloud-dlp/setup.py
index 46183550feb5..52fe893a6e32 100644
--- a/packages/google-cloud-dlp/setup.py
+++ b/packages/google-cloud-dlp/setup.py
@@ -27,7 +27,7 @@
     # 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 >= 0.4.0",
     "pytz >= 2021.1",
 ]
diff --git a/packages/google-cloud-dlp/testing/constraints-3.6.txt b/packages/google-cloud-dlp/testing/constraints-3.6.txt
index 79536abc8856..b971d2456871 100644
--- a/packages/google-cloud-dlp/testing/constraints-3.6.txt
+++ b/packages/google-cloud-dlp/testing/constraints-3.6.txt
@@ -5,6 +5,6 @@
 #
 # 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==0.4.0
 libcst==0.2.5