The 62-year-old man was cycling along Braes Road in Saltcoats when the driver caused him to brake suddenly, causing serious injuries.
The car drove off after the incident at 1.20pm on Thursday, leaving the cyclist in the road.
He was taken by ambulance to Crosshouse Hospital near Kilmarnock for treatment to his injuries, which are not said to be life threatening.
The driver was a white man, aged between 25 and 35 and of medium build.
He was last seen wearing a white or light-coloured top and shorts, dark jacket and a dark baseball cap.
The car was small black or dark hatchback.
Police Sergeant Kevin Blackley said: “Our inquiries into the circumstances of the incident are ongoing.
“Anyone who witnessed the incident or has dashcam footage which may assist the investigation is asked to contact police on 101, quoting 1464 of 29 April.”