North Yorkshire Police said a heavy goods vehicle (HGV) with a white trailer attached had collided with a silver Nissan Juke.
The HGV did not stop at the scene and police believe the driver may be unaware that they were involved in a collision.
It happened at around 1.20am on the northbound carriageway between junction 47 (Allerton Park) and junction 48 (Boroughbridge).
A spokesman said: "Officers are appealing to HGV drivers who were on the A1 northbound around the time and place of the collision to contact them.
"The occupants of the Nissan - a man, woman and two children - were uninjured.
"The central barrier of the motorway was slightly damaged as a result of the collision."
The driver and anyone else who witnessed the collision or who can help to identify the HGV involved are asked to contact North Yorkshire Police.
Email [email protected] or call 101, select option 2 and ask for Traffic Constable Chris Garbutt.
Please quote reference 12170218624 when passing on information.