A police source said his injuries from the crash were thought to be very serious at first, but later it appeared he suffered a number of broken ribs and cuts and bruises.
The accident happened at about 6pm yesterday in Wrightington, Lancashire, which is near to his family home in Eccleston.
Father-of-two Wiggins is known to regularly embark on training rides around the area's rural roads.
The driver of the Astra, a local woman, was uninjured.
A Lancashire Police spokesman said last night: "Police were called to the scene of a road traffic accident at Crow Orchard Road in Wrightington at about 6pm this evening.
"A cyclist has been involved in a collision with a white Vauxhall Astra car. The rider of the bike, a 32-year-old local man, was taken to hospital by ambulance with injuries not thought to be life-threatening. His family have been told."
Collision investigators visited the scene but the road did not need to be closed.
Garage attendant Yasmin Smith, who rushed to Wiggins'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."
"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.
"We will announce more details in due course."
Ms Smith told ITV's Daybreak she was in the garage's office when she heard a screeching of tyres and a loud bang, so rushed outside to help.
She said: "I came straight outside to see a gentleman sat on the pavement, but I didn't realise who he was. I just went over to help. The ambulance and the police had been called."
Ms Smith said the driver was in shock. She said: "She was very upset, even more upset when the police actually said 'do you realise who you've hit?'.
"That really put her back, because obviously she felt bad enough."
Ms Smith said Wiggins's wife Cath was on the scene within about five minutes.
A broken wing mirror thought to be from the Vauxhall was laying on a grass verge near the exit of the petrol station.