The woman, who was driving a silver Volkswagen Golf, was taken to hospital - but her injuries are not believed to be life-threatening.
Three officers in the Land Rover were also hurt in the crash, which happened at about 6.15am.
The Police Ombudsman's Office has been informed and is appealing for witness to contact them.
"The collision happened on the A6 Glenshane Road, close to the Watty Graham's Glen Gaelic Club, about a mile from Maghera," a spokesman for the Ombudsman's office said.
"The Land Rover was one of two similar police vehicles travelling south, while the Volkswagen was travelling in the opposite direction.
"Our investigators are co-ordinating forensic enquiries, photography at the scene, and interviews of witnesses."
The spokesman added: "We are keen to hear from anyone who might have seen what happened, or who believes they might have information to assist our efforts to establish how this collision occurred."
Anyone who has information is asked to call the free-phone witness appeal line on 0800 032 7880.