The collision happened at about 12:35 GMT at Tamnamore, between junctions 13 and 14.
The motorway has been closed in both directions, which has caused long traffic tailbacks.
Police are advising motorists heading to Belfast to exit at junction 15.
Motorists heading in the Enniskillen in County Fermanagh direction should exit at junction 12 and travel by Armagh city.
Police are urging anyone who witnessed the crash or saw the man's Honda Civic before the collision to contact them on the non-emergency number 101.
A man has been killed in a car crash on the M1 in County Tyrone.