Emergency services were called to the scene between junctions 32 (for Broughton) and 33 (for Lancaster) on the northbound carriageway just before 1am on Monday morning.
Two police officers who were described as "walking wounded" were taken to hospital for precautionary checks.
A spokesman for the police said: "A police car had a blown out tyre and crashed into the barriers.
"The police officers went to hospital for checks but are not believed to have been seriously injured.
"The motorway was closed to allow for investigations to take place.
"No other vehicles were involved."
The motorway re-opened at around 5.30am.