It happened at around 1.20am on the northbound carriageway between junction 47 (Allerton Park) and junction 48 (Boroughbridge) when a HGV with a white trailer attached collided with a silver Nissan Juke.
The HGV did not stop at the scene and the driver may be unaware that they were involved in a collision.
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 can help identify the HGV involved is asked to contact North Yorkshire Police on 101, select option 2 and ask for Traffic Constable Chris Garbutt or email Chris.Garbutt@northyorkshire.police.pnn.uk
Please quote reference 12170218624 when passing on information.