Police said the man, in his 80s, was involved in an altercation yesterday (Thursday) with an elderly couple in Sainsbury's car park on Wetherby Road.
He fell to the ground following the altercation with the couple, who were in a blue vehicle at the time.
The man was treated by ambulance staff at the scene at about 5.30pm yesterday.
A North Yorkshire Police spokesperson said: "Officers are conducting enquiries and are requesting the public’s assistance to help determine the full circumstances surrounding the incident, in particular any witnesses and also the manner of driving and behaviour of the pedestrian prior to the incident."
Anyone with information is asked to call police on 101, quoting NYP-16112017-0395 when sharing information.