West Yorkshire Police said a blue Ford Iveco horsebox was involved in collision with a grey Audi A1 on the westbound M62 near Cleckeheaton.
As a result of the collision, the Audi went onto the hard shoulder where it struck the barriers.
The Audi driver required hospital treatment. The horsebox did not stop at the scene
The incident happened at around 4.15pm on Wednesday December 28, but police only released details today. (Tues Jan 3)
The vehicle officers want to trace is described as having the word "horses" written on the side in yellow or gold writing.
The driver of the horsebox, or anyone with information about it or who witnessed the manner in which it was being driven immediately prior to the incident, are asked to contact PC Bob Hoyle on 101 quoting log 954 of 28 December.