The striker posted the claim on his Twitter feed shortly after the match, which was settled by Hugo Rodallega's 76th-minute goal.
Bent's original post read: "So we get beaten by Wigan and to make matters worse my mum gets racially abused by a Sunderland fan. I won't stand for that."
In later posts replying to other users of the site, Bent labelled the abuse "an absolute disgrace" and warned: "The offender needs to hope I don't find out his name or who he is".
The matter has been reported to the police, with a club spokeswoman confirming to BBC Sport: "Sunderland are liaising with Northumbria Police to fully investigate this matter.
"Behaviour of this kind is totally unacceptable to our football club."