diff --git a/docs/middleware.md b/docs/middleware.md
index a91342744..92ac5886a 100644
--- a/docs/middleware.md
+++ b/docs/middleware.md
@@ -106,6 +106,8 @@ The following arguments are supported:
 * `max_age` - Session expiry time in seconds. Defaults to 2 weeks. If set to `None` then the cookie will last as long as the browser session.
 * `same_site` - SameSite flag prevents the browser from sending session cookie along with cross-site requests. Defaults to `'lax'`.
 * `https_only` - Indicate that Secure flag should be set (can be used with HTTPS only). Defaults to `False`.
+* `domain` - Domain of the cookie used to share cookie between subdomains or cross-domains. The browser defaults the domain to the same host that set the cookie, excluding subdomains [refrence](https://developer.mozilla.org/en-US/docs/Web/HTTP/Cookies#domain_attribute). 
+
 
 ## HTTPSRedirectMiddleware
 
diff --git a/starlette/middleware/sessions.py b/starlette/middleware/sessions.py
index 74e57352f..1093717b4 100644
--- a/starlette/middleware/sessions.py
+++ b/starlette/middleware/sessions.py
@@ -20,6 +20,7 @@ def __init__(
         path: str = "/",
         same_site: typing.Literal["lax", "strict", "none"] = "lax",
         https_only: bool = False,
+        domain: typing.Optional[str] = None,
     ) -> None:
         self.app = app
         self.signer = itsdangerous.TimestampSigner(str(secret_key))
@@ -29,6 +30,8 @@ def __init__(
         self.security_flags = "httponly; samesite=" + same_site
         if https_only:  # Secure flag can be used with HTTPS only
             self.security_flags += "; secure"
+        if domain is not None:
+            self.security_flags += f"; domain={domain}"
 
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         if scope["type"] not in ("http", "websocket"):  # pragma: no cover
diff --git a/tests/middleware/test_session.py b/tests/middleware/test_session.py
index 3f43506c4..8500f7b54 100644
--- a/tests/middleware/test_session.py
+++ b/tests/middleware/test_session.py
@@ -178,3 +178,27 @@ def test_session_cookie(test_client_factory):
     client.cookies.delete("session")
     response = client.get("/view_session")
     assert response.json() == {"session": {}}
+
+
+def test_domain_cookie(test_client_factory):
+    app = Starlette(
+        routes=[
+            Route("/view_session", endpoint=view_session),
+            Route("/update_session", endpoint=update_session, methods=["POST"]),
+        ],
+        middleware=[
+            Middleware(SessionMiddleware, secret_key="example", domain=".example.com")
+        ],
+    )
+    client: TestClient = test_client_factory(app)
+
+    response = client.post("/update_session", json={"some": "data"})
+    assert response.json() == {"session": {"some": "data"}}
+
+    # check cookie max-age
+    set_cookie = response.headers["set-cookie"]
+    assert "domain=.example.com" in set_cookie
+
+    client.cookies.delete("session")
+    response = client.get("/view_session")
+    assert response.json() == {"session": {}}