Sunderland's League One rivals Bolton Wanderers suffer injury blow after car crash
Wanderers said in a statement on their official website on Monday that the 25-year-old left-back had sustained broken ribs and a broken collarbone and was being supported by the club's medical staff.
It is not yet known how long he will be out for.
The statement added: "He will remain in hospital for the next 48 hours as a precautionary measure.
"Everybody at Bolton Wanderers wishes Joe a quick recovery."
Bunney was among the nine players Bolton signed on transfer deadline day last week, joining from Northampton until the end of the season. The move reunited him with boss Keith Hill, who he had worked under at Rochdale.
Sunderland, who return to League One action away to Accrington Stanley on Saturday, play Bolton away on September 21.