Wright was involved in an aerial challenge with Andre Dozzell just after the hour mark, when he received a knock from a stray elbow which left him lying prone on the ground.
A short time later the 28 year-old left the pitch in a medi-cab.
"I think he was a little bit dazed, but I don't think it was concussion," Sunderland manager Lee Johnson said of Wright. "He's got a cut to his mouth. He was an absolute warrior."
Sunderland held on to record an important 1-0 win, thanks to Charlie Wyke's neatly-taken first half goal, Ipswich having been reduced to 10 men early on after Kayden Jackson saw red for a clumsy challenge.