diff --git a/google/cloud/bigquery_storage_v1/reader.py b/google/cloud/bigquery_storage_v1/reader.py
index 2e387eb2..0677316c 100644
--- a/google/cloud/bigquery_storage_v1/reader.py
+++ b/google/cloud/bigquery_storage_v1/reader.py
@@ -712,7 +712,7 @@ def to_rows(self, message):
                 # TODO: Parse DATETIME into datetime.datetime (no timezone),
                 #       instead of as a string.
                 yield fastavro.schemaless_reader(messageio, self._fastavro_schema)
-            except StopIteration:
+            except (StopIteration, EOFError):
                 break  # Finished with message