diff --git a/pandas_gbq/features.py b/pandas_gbq/features.py
index 2871d5ea..62405b4c 100644
--- a/pandas_gbq/features.py
+++ b/pandas_gbq/features.py
@@ -5,7 +5,7 @@
 """Module for checking dependency versions and supported features."""
 
 # https://github.com/googleapis/python-bigquery/blob/main/CHANGELOG.md
-BIGQUERY_MINIMUM_VERSION = "3.3.5"
+BIGQUERY_MINIMUM_VERSION = "3.4.2"
 BIGQUERY_QUERY_AND_WAIT_VERSION = "3.14.0"
 PANDAS_VERBOSITY_DEPRECATION_VERSION = "0.23.0"
 PANDAS_BOOLEAN_DTYPE_VERSION = "1.0.0"
diff --git a/setup.py b/setup.py
index 461cbfde..df793e59 100644
--- a/setup.py
+++ b/setup.py
@@ -23,7 +23,7 @@
 dependencies = [
     "setuptools",
     "db-dtypes >=1.0.4,<2.0.0",
-    "numpy >=1.16.6",
+    "numpy >=1.18.1",
     "pandas >=1.1.4",
     "pyarrow >=3.0.0",
     "pydata-google-auth >=1.5.0",
@@ -35,8 +35,8 @@
     "google-auth-oauthlib >=0.7.0",
     # Please also update the minimum version in pandas_gbq/features.py to
     # allow pandas-gbq to detect invalid package versions at runtime.
-    "google-cloud-bigquery >=3.3.5,<4.0.0dev",
-    "packaging >=20.0.0",
+    "google-cloud-bigquery >=3.4.2,<4.0.0dev",
+    "packaging >=22.0.0",
 ]
 extras = {
     "bqstorage": [
diff --git a/testing/constraints-3.8.txt b/testing/constraints-3.8.txt
index f77e0f2d..e551d17e 100644
--- a/testing/constraints-3.8.txt
+++ b/testing/constraints-3.8.txt
@@ -10,11 +10,11 @@ db-dtypes==1.0.4
 google-api-core==2.10.2
 google-auth==2.13.0
 google-auth-oauthlib==0.7.0
-google-cloud-bigquery==3.3.5
+google-cloud-bigquery==3.4.2
 google-cloud-bigquery-storage==2.16.2
-numpy==1.16.6
+numpy==1.18.1
 pandas==1.1.4
 pyarrow==3.0.0
 pydata-google-auth==1.5.0
 tqdm==4.23.0
-packaging==20.0.0
\ No newline at end of file
+packaging==22.0.0
\ No newline at end of file