West Yorkshire Police said the M606 in Bradford is currently closed in both directions due to the serious collision which happened at around 10.45pm on June 13.
A Ford Transit van had failed to stop for one of the force's roads policing unit and then drove the wrong way down the southbound carriageway, from Chain Bar roundabout towards Bradford, when it was involved in a head on crash with a taxi.
Five people have been injured, and three are in a critical condition, the force said.
A statement said: "The M606 is currently closed in both directions while emergency services respond to the incident.
"The scene and road closures are expected to be in place for a significant period and drivers are advised to avoid the area and seek alternative routes.
"West Yorkshire Police has informed the Independent Office for Police Conduct due to the involvement of a police vehicle in the circumstances leading up to the collision."
Highways England said investigation work on the carriageway is likely to go on throughout the morning.
An IOPC statement said: "The Independent Office for Police Conduct (IOPC) is carrying out an independent investigation into the involvement of West Yorkshire Police (WYP) prior to a road traffic collision on the M606 near the Chain Bar roundabout, Bradford, at around 10.45pm on Monday 13 June.
"We were notified by WYP after the collision and an independent investigation declared at 12.51am today (Tuesday 14 June).
"We understand that a Ford Transit van failed to stop for police before it was involved in a collision with a taxi after the van entered the M606 on the wrong side of the carriageway.
"IOPC investigators are attending the scene and the police post incident procedure. We have begun to gather information and our investigation is at an early stage."
The road reopened at around 10.30am.