The smash happened on Oldham Road, close to the junction with the M60 in Hollinwood, just after 10pm last night.
Greater Manchester Police (GMP) said the patrol car was responding to a 'grade one' call.
Grade One is the most serious category of incident.
The road was closed travelling towards Oldham while emergency services dealt with the aftermath and subsequent clean-up operation.
GMP reportedly said three people were involved, two of whom were police officers.
However, none were said to have been seriously injured.
The second car involved is understood to have been a red Mazda.
It has since been confirmed that no-one has been arrested in connection with the incident.
