Gov. Andrew Cuomo announced the bridge closing around midday Sunday. The Tappan Zee's northbound lanes had already closed, and closures of parts of the Thruway had cut off access to the southbound lanes.
Hudson River bridges north of the Tappan Zee Bridge remain open, with moderate sustained winds.
The northbound Thruway is closed between Tarrytown and Harriman. The highway is closed southbound between Newburgh and West Nyack.
Drivers are advised to seek alternate routes.
The Thruway has been dealing with scattered flooding, fallen tree limbs and a mudslide.