It is understood he was on his way to work when the incident happened between the Lurgan and Portadown junctions of the M1 motorway in Co. Armagh at about 7:30am.
The Police Service of Northern Ireland (PSNI) say they have not yet confirmed the cause of his death.
The car careered off the road and the man died later.
Police say his family has not yet been informed.
It happened on the eastbound section of motorway which is closed in both directions.
Cause of death unclear
The DUP assembly member Paul Givan says the man was on his way to work in Antrim when the shooting happened.
A spokesperson for the PSNI said "Police believe from an examination of the scene on the motorway that shots may have been fired at the vehicle".
However they cannot confirm whether the man died as a result of the shots fired or the resulting collision.
