diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 83ab72737..0b70ffc64 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -310,6 +310,16 @@ jobs:
     needs: linting-done
     runs-on: ubuntu-latest
 
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - arrangement: monolith
+            database: SQLite
+
+          - arrangement: monolith
+            database: Postgres
+
     steps:
       # The path is set via a file given by $GITHUB_PATH. We need both Go 1.17 and GOPATH on the path to run Complement.
       # See https://docs.github.com/en/actions/using-workflows/workflow-commands-for-github-actions#adding-a-system-path
@@ -337,7 +347,7 @@ jobs:
 
       - run: |
           set -o pipefail
-          COMPLEMENT_DIR=`pwd`/complement synapse/scripts-dev/complement.sh -json 2>&1 | gotestfmt
+          POSTGRES=${{ (matrix.database == 'Postgres') && 1 }} COMPLEMENT_DIR=`pwd`/complement synapse/scripts-dev/complement.sh -json 2>&1 | gotestfmt
         shell: bash
         name: Run Complement Tests
 
diff --git a/changelog.d/12965.misc b/changelog.d/12965.misc
new file mode 100644
index 000000000..cc2823e12
--- /dev/null
+++ b/changelog.d/12965.misc
@@ -0,0 +1 @@
+Enable testing against PostgreSQL databases in Complement CI.
\ No newline at end of file