The accident happened on the Coolkill Road in Middletown in Co Armagh.
Police say one man was removed from the vehicle with injuries which are not believed to be life-threatening.
The NI Ambulance Service said it dispatched an accident an emergency vehicle along with a rapid response paramedic and a doctor to the scene.
The road remains blocked. An investigation is being carried out.
Last week, a man died after the van he was trying was killed by a falling tree.
The accident happend on the Keady Road in Armagh.
A woman, who was a passenger in the van, was taken to hospital for emergency treatment.
Meanwhile in Ballymena, the Crankill Road is blocked by a fallen tree close to Ashgrove Conservatories.
Police are advising motorists to avoid the area or expect delays.
The Met Office have said that Tuesday night will see further showers with snow falling in areas of higher ground.
The showers will be mostly in the north and west extending to many places later.
Strong to gale force northwest winds are expected especially along the north coast with a minimum temperature of three degrees.