The incident happened just before 4 o'clock on the Gartan stage close to Termon.
The man was injured when a car left the road - it is not clear if he was struck by the vehicle or debris thrown up by it.
The injured man who is a service crew member received treatment at the scene before being transferred to hospital. His injuries are not life threatening.
The incident happened on stage 12, which was then cancelled. The event resumed at stage 13 but the second running of the Gartan stage was also cancelled.
The Donegal Motor Club released a statement this evening saying - "The organisers of the Donegal International Rally Ireland have confirmed the cancellation of Special Stage 14 of the event as a result of time delays caused by previous incidents.
A spokesman said there was an accident on special stage 12, when a competing car went off the road, resulting in the emergency services being deployed. The competing crew were attended to and suffered no serious injuries.
A member of a rally service crew was injured and removed to Letterkenny General Hospital where his condition is being assessed. The investigation of the incident is ongoing, but it is believed that the competing car may not have come into direct contact with the person involved.
Shortly afterwards in a separate incident in the same area a local person became unwell and rally medical services, including an ambulance, were deployed to assist.
The competing cars were rerouted back to service and the organisers later decided to cancel special stage 14, the last stage of the day, as a result of the time losses incurred."