The accident happened around four in the morning at the intersection of Valencia's Tres Forques and Llanterners streets.
A police patrol car rammed into a Ford Focus whose driver was not at fault, reported Las Provincias newsaper.
The police vehicle then bounced over a raised median strip and slammed into another car that was waiting at the traffic lights.
Several cars from national and local police forces were quickly on the scene.
Preliminary investigations show the police car drove through a red light with its flashing light on.
Its driver was apparently rushing to a gaming parlour where a knife fight had broken out.
"I started driving when the light turned green and couldn't stop," said Johnathon C., the uninjured driver of the Ford Focus.
His girlfriend, meanwhile, ended up in hospital.
The two passengers in the other car were also injured, as were the two police officers who caused the accident.