Both directions of the motorway between junction 36 and 37 have been closed this morning after the collision and could be shut for a "significant" amount of time, officers said at around 11am.
Police, other emergency services and traffic officers are at the scene, the authority added.
A spokesperson for Humberside Police said: "We are currently in attendance at a serious road traffic collision on the M62 motorway between Junctions 36 and 37 near to Goole.
"A lorry which was travelling westbound had gone through the central reservation and collided with an oncoming car which was travelling eastbound."
"Both carriageways are closed while emergency crews are on the scene. They are expected to be closed for a significant amount of time throughout today."
"Motorists are advised to avoid the area. Diversions are in place.
"We understand that drivers have already been caught up in traffic jams leading up to the collision. We would ask them to be patient and remain in their vehicles for safety reasons and to allow emergency services to carry out their work."
Diversions have been put in place for drivers on both carriageways and motorists have been urged to allow extra time for their journeys.