The British Boxing Board of Control are set to investigate the incident after both fighters fell to the floor, with Price emerging with a clear bite mark on his chest.
Referee Mark Lyson immediately stopped the contest and disqualified Ali, who had earlier been docked a point for punching to the back of the head, and whom Price also accused of biting his arm earlier in the contest.
On the same card former WBO light-middleweight champion Liam Smith outclassed his former sparring partner Sam Eggington, whose corner threw in the towel in the fifth round of a one-sided contest.
Meanwhile Rio Olympian Antony Fowler lost his unbeaten professional record to former Great Britain team-mate Scott Fitzgerald, who triumphed via split decision after 10 tumultuous rounds.
Fowler, a heavy favourite, started on top before Fitzgerald took over in the middle part of the contest to build a slender points lead.
Fowler had a strong ninth round, rattling Fitzgerald with a big uppercut, but the Preston man reacted superbly in the last as he dropped Fowler to scrape home 95-94 (twice), with the third judge scoring 96-94 for Fowler.
Price admitted his win over Ali was far from satisfactory but will now look to press on and rebuild his career after a series of recent setbacks.
Speaking in the ring, the fight broadcast on Sky Sports, Price was asked about a rematch, but he said: "I don't want to share a ring with an animal like that again."
Former world cruiserweight champion Tony Bellew branded Ali "a disgrace" and called for him to be banned.