The Premier League player's Bentley Continental was in collision with the unmarked police Ford Mondeo which was responding to an emergency call last night in Stockport, Cheshire.
Neither drivers were hurt but the passenger in the police car, a special constable, received minor injuries, Greater Manchester Police (GMP) said.
In line with normal procedure after an accident the police driver has been suspended until an investigation is carried out.
The force said only minor damage was caused to the police car and Nani's Bentley - which cost up to £180,000.
The midfielder, a Portuguese international signed by Manchester United in 2007 for £25.5 million, was reportedly still in his training kit and returning home when the collision happened.
A spokeswoman for GMP said: "At about 6.40pm on Friday 15 February 2013, an unmarked police car responding to an emergency call was travelling along Gatley road at the junction with Kingsway, Stockport.
"As the police car entered the junction it collided with a Bentley, Continental.
"The passenger in the police car received minor injuries and only minor damage was caused to both vehicles.
"The police driver has been suspended from driving duties in line with normal procedure.
"Anyone with information should call police on 0161 856 4741."