The crash happened at about 4.50pm on Wednesday, in Seamer Road.
It involved a cyclist and a white BMW or Audi car.
A North Yorkshire Police spokesman said: "It is believed the actions of the BMW/Audi may have caused the cyclist to come off their bike.
"As a result of the collision, the cyclist, a 49-year-old local man, suffered a number of injuries including two broken ribs, a ruptured rotator cuff and mild concussion.
"We are appealing for witnesses to the collision or anyone who recalls seeing the vehicle(s) prior to the collision to get in touch as soon as possible to assist the investigation."
Anyone with information is asked to call police on 101, quoting reference number NYP-23092018-0365.