Wiggins, 32, was thought to have suffered broken ribs and a dislocated finger as he was thrown off his bike near his home in Lancashire on Wednesday night.
However, sources said he had now been discharged following the accident.
Wiggins was taken by ambulance to Royal Preston Hospital following the crash in Crow Orchard Road, Wrightington, shortly after 6pm.
The incident happened when the driver of a white Vauxhall Astra Envoy, a local woman, drove out of a garage forecourt.
Police said they intended to speak to the driver on Thursday, who was uninjured, as part of their inquiries.
Wiggins was driven to his home in Eccleston on Thursday afternoon after he reportedly underwent scans to assess the full extent of his injuries.
Cycling journalist William Fotheringham, who helped write Wiggins' new autobiography, reported the Olympic gold medallist was also given morphine and a precautionary scan of his head in hospital.
Father-of-two Wiggins was due to attend a number of interviews to promote his book My Time, which was published on Thursday.
He was to have appeared on the Chris Evans show on BBC Radio 2 and later record an item for The Graham Norton Show on BBC1 to be broadcast on Friday night, when other guests are due to be Cameron Diaz and Rod Stewart.
Wiggins was also scheduled to take part in a webchat with The Guardian which has serialised extracts of his autobiography this week.
Fotheringham, writing in The Guardian, reported that Wiggins was riding a mountain bike to meet a group of local cyclists near his home.
Wiggins was planning to resume his winter training for next year's racing programme after an autumn break, he added.
In a statement on its website, Team Sky said: "We can confirm that on Wednesday evening Bradley Wiggins was involved in a road traffic accident whilst riding his bike near his home in Lancashire.
Garage attendant Yasmin Smith went to Wiggins' aid when she heard a screech of tyres and a loud bang.
She told ITV's Daybreak: "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 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' wife Cath was on the scene within about five minutes.
AA president Edmund King said: "This collision should act as a reminder to all drivers that we need to be more vigilant, particularly when pulling out of entrances and turning at junctions.
"With autumnal weather and darker evenings it is essential to check and double check for cyclists, pedestrians and indeed other road users before pulling out.
"We need to break down the 'two tribe' mentality on the roads and co-exist in harmony."