diff --git a/.changes/unreleased/Fixes-20241001-193207.yaml b/.changes/unreleased/Fixes-20241001-193207.yaml
new file mode 100644
index 000000000..584445a5b
--- /dev/null
+++ b/.changes/unreleased/Fixes-20241001-193207.yaml
@@ -0,0 +1,7 @@
+kind: Fixes
+body: Catch additional database error exception, NotFound, as a DbtDatabaseError instead
+  of defaulting to a DbtRuntimeError
+time: 2024-10-01T19:32:07.304353-04:00
+custom:
+  Author: mikealfare
+  Issue: "1360"
diff --git a/dbt/adapters/bigquery/connections.py b/dbt/adapters/bigquery/connections.py
index f96bc1381..afe609a5a 100644
--- a/dbt/adapters/bigquery/connections.py
+++ b/dbt/adapters/bigquery/connections.py
@@ -254,6 +254,10 @@ def exception_handler(self, sql):
             message = "Access denied while running query"
             self.handle_error(e, message)
 
+        except google.cloud.exceptions.NotFound as e:
+            message = "Not found while running query"
+            self.handle_error(e, message)
+
         except google.auth.exceptions.RefreshError as e:
             message = (
                 "Unable to generate access token, if you're using "