diff --git a/packages/google-cloud-bigquery/google/cloud/bigquery/_arrow_query.py b/packages/google-cloud-bigquery/google/cloud/bigquery/_arrow_query.py
index ca98bc18f39d..443f5c5d4e91 100644
--- a/packages/google-cloud-bigquery/google/cloud/bigquery/_arrow_query.py
+++ b/packages/google-cloud-bigquery/google/cloud/bigquery/_arrow_query.py
@@ -81,10 +81,9 @@ def _check_dependencies() -> None:
     _versions_helpers.BQ_STORAGE_VERSIONS.try_import(raise_if_error=True)
     if not _versions_helpers.BQ_STORAGE_VERSIONS.supports_arrow_serialization_options:
         raise exceptions.LegacyBigQueryStorageError(
-            "query_results_format=ARROW needs a google-cloud-bigquery-storage "
-            "release whose BigQueryReadClient.read_rows() accepts "
-            "arrow_serialization_options, please upgrade it "
-            "(`pip install --upgrade google-cloud-bigquery-storage`) "
+            "query_results_format=ARROW needs a newer google-cloud-bigquery-storage, "
+            "please upgrade it "
+            '(`pip install "google-cloud-bigquery[bqstorage]"`) '
             "(version found: "
             f"{_versions_helpers.BQ_STORAGE_VERSIONS.installed_version})."
         )
diff --git a/packages/google-cloud-bigquery/pyproject.toml b/packages/google-cloud-bigquery/pyproject.toml
index 82d8e2219eee..b0936b70c72b 100644
--- a/packages/google-cloud-bigquery/pyproject.toml
+++ b/packages/google-cloud-bigquery/pyproject.toml
@@ -60,7 +60,7 @@ Repository = "https://github.com/googleapis/google-cloud-python/tree/main/packag
 # moved back to optional due to bloat.  See
 # https://github.com/googleapis/python-bigquery/issues/1196 for more background.
 bqstorage = [
-  "google-cloud-bigquery-storage >= 2.29.0, < 3.0.0",
+  "google-cloud-bigquery-storage >= 2.43.0, < 3.0.0",
   # Due to an issue in pip's dependency resolver, the `grpc` extra is not
   # installed, even though `google-cloud-bigquery-storage` specifies it
   # as `google-api-core[grpc]`. We thus need to explicitly specify it here.
diff --git a/packages/google-cloud-bigquery/testing/constraints-3.10.txt b/packages/google-cloud-bigquery/testing/constraints-3.10.txt
index d9c428673b02..4f8a652e1312 100644
--- a/packages/google-cloud-bigquery/testing/constraints-3.10.txt
+++ b/packages/google-cloud-bigquery/testing/constraints-3.10.txt
@@ -5,7 +5,7 @@ google-resumable-media==2.0.0
 packaging==24.2.0
 python-dateutil==2.8.2
 requests==2.33.0
-google-cloud-bigquery-storage==2.29.0
+google-cloud-bigquery-storage==2.43.0
 grpcio==1.59.0
 grpcio-status==1.59.0
 pyarrow==6.0.0
diff --git a/packages/google-cloud-bigquery/tests/unit/test_query_results_format_arrow.py b/packages/google-cloud-bigquery/tests/unit/test_query_results_format_arrow.py
index 1855d854c470..4f55169b8622 100644
--- a/packages/google-cloud-bigquery/tests/unit/test_query_results_format_arrow.py
+++ b/packages/google-cloud-bigquery/tests/unit/test_query_results_format_arrow.py
@@ -774,7 +774,7 @@ def test_check_dependencies_requires_read_rows_arrow_options(supported):
         else:
             with pytest.raises(
                 exceptions.LegacyBigQueryStorageError,
-                match=r"pip install --upgrade google-cloud-bigquery-storage.*"
+                match=r'pip install "google-cloud-bigquery\[bqstorage\]".*'
                 r"\(version found: 2\.42\.0\)",
             ):
                 _check_dependencies()