Khan, 22, was behind the wheel of his Range Rover when the accident happened in his home town of Bolton on Sunday night.
The cyclist suffered a head injury and was taken to hospital. His injuries are not thought to be serious.
A spokeswoman for Greater Manchester Police said: "At 9.40pm on Sunday 12 July 2009, police were called to Moor Lane, Bolton, following reports of a road traffic collision.
"Officers attended and discovered a Range Rover had collided with a cyclist.
"The cyclist suffered a head injury in the collision and was taken to hospital by ambulance for treatment.
"His injuries are not believed to be life threatening.
"No one else was injured in the collision.
"Inquiries are ongoing."
Khan, who first shot to fame as a teenager by winning a silver medal at the Athens Olympics in 2004, has twice been in trouble with police over his driving.
In October 2007 he was convicted of careless driving after he went through a red light and injured a pedestrian.
He was driving his £87,000 BMW convertible in Bradshawgate, Bolton, when he struck Geoffrey Hatton on a pelican crossing. Mr Hatton, 55, suffered a broken leg in the incident.
Khan was cleared of dangerous driving, but found guilty of careless driving. He was given a six-month driving ban and fined £1,000.
Three months later he was back in court to face magistrates for an earlier offence of speeding.
A police officer said his own speedometer was "off the clock" at 155mph as he pursued the boxer on the M62 motorway near Rochdale.
He was fined £1,000 and banned for 42 days for speeding in his BMW.
On Saturday Khan will fight Andreas Kotelnik for the WBA world welterweight title in Manchester, his first attempt to win a world title.
