The Scottish international will not be considered for selection for Saturday's Barclays Premier League clash at Sunderland. Bannan was arrested by police on suspicion on drink driving - along with Shrewsbury striker James Collins, a former Villa player - and subsequently bailed.
Villa boss Alex McLeish, in a media statement, said: "Barry Bannan has been suspended while the club carries out internal enquiries into allegations which arose last weekend. He will not be available for this weekend's game at Sunderland."
The accident occurred on the M1 at around 5.30am on Sunday, near junction 26.
Villa confirmed on Monday that they had launched the investigation and have now opted to suspend Bannan.
The 21-year-old is regarded as one of Villa's brightest prospects and has made an encouraging start to the current campaign.
He has already won nine caps for his country.
Collins joined Shrewsbury from Villa during the 2011 January transfer window.
Police had already confirmed that two men had been bailed after being arrested in connection with the accident involving a Range Rover on the southbound carriageway.