Wiggins, 32, who also won gold in the time trial at this summer's London 2012 Olympics, was involved in a collision with a car near his home in Eccleston, Lancashire.
The Team Sky cyclist is understood to have broken several ribs and suffered hand and wrist injuries.
The incident happened at 6pm when a white Vauxhall Astra car pulled off a filling station forecourt and collided with the cyclist.
Garage attendant Yasmin Smith, who rushed to the champion's aid, said: "By the time I got there he had moved to a safer place, but was still on the ground and he was in a lot of pain.
"He said he thought he had broken his ribs and while a lot of police cars arrived, it was about 15 minutes before the ambulance got there by which time he was blue."
In a statement, Team Sky said: "He is being kept in hospital overnight for observation but the injuries he has sustained are not thought to be serious and he is expected to make a full and speedy recovery."