diff --git a/datasette/database.py b/datasette/database.py
index e908d1ea..06dc8da5 100644
--- a/datasette/database.py
+++ b/datasette/database.py
@@ -345,7 +345,9 @@ class Database:
                     """
                 select name from sqlite_master
                 where rootpage = 0
-                and sql like '%VIRTUAL TABLE%USING FTS%'
+                and (
+                    sql like '%VIRTUAL TABLE%USING FTS%'
+                ) or name in ('sqlite_stat1', 'sqlite_stat2', 'sqlite_stat3', 'sqlite_stat4')
             """
                 )
             ).rows
diff --git a/tests/test_api.py b/tests/test_api.py
index 574ebb41..47ec3a8c 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -1030,3 +1030,15 @@ async def test_db_path(app_client):
 
     # Previously this broke if path was a pathlib.Path:
     await datasette.refresh_schemas()
+
+
+@pytest.mark.asyncio
+async def test_hidden_sqlite_stat1_table():
+    ds = Datasette()
+    db = ds.add_memory_database("db")
+    await db.execute_write("create table normal (id integer primary key, name text)")
+    await db.execute_write("create index idx on normal (name)")
+    await db.execute_write("analyze")
+    data = (await ds.client.get("/db.json?_show_hidden=1")).json()
+    tables = [(t["name"], t["hidden"]) for t in data["tables"]]
+    assert tables == [("normal", False), ("sqlite_stat1", True)]