diff --git a/setup.py b/setup.py
index 7f72131638..1738eed2ea 100644
--- a/setup.py
+++ b/setup.py
@@ -37,7 +37,7 @@
 
 dependencies = [
     "google-api-core[grpc] >= 1.34.0, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*,!=2.8.*,!=2.9.*,!=2.10.*",
-    "google-cloud-core >= 1.4.1, < 3.0dev",
+    "google-cloud-core >= 1.4.4, < 3.0dev",
     "grpc-google-iam-v1 >= 0.12.4, <1.0.0dev",
     "proto-plus >= 1.22.0, <2.0.0dev",
     "sqlparse >= 0.4.4",
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index cddc7be6e5..165814fd90 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -5,7 +5,7 @@
 # e.g., if setup.py has "google-cloud-foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have google-cloud-foo==1.14.0
 google-api-core==1.34.0
-google-cloud-core==1.4.1
+google-cloud-core==1.4.4
 grpc-google-iam-v1==0.12.4
 libcst==0.2.5
 proto-plus==1.22.0