Udinese had the better of the first-half chances, but the league leaders broke the deadlock in the 29th minute with their only other meaningful attack of the opening period, with Portugal forward Rafael Leao firing home.
The visitors continued to press after the break and deservedly levelled through Destiny Udogie in the 66th minute.
Leao had Milan's best chance to win it late on, but his lofted effort was cleared off the line much to the San Siro's frustration, with Udinese otherwise continuing to look the most threatening until the final whistle.
Milan have now won only two of their last six league games, with their coach Stefano Pioli unhappy with the goal that denied his side a much-needed victory over Udinese, accusing Udogie of using his hand when bundling the equaliser home.
"In my opinion it is not a dubious goal, it is evident that he scored by using a hand," Pioli told DAZN. "The referee did not see, but that why did the VAR not see it?
"The VAR exists to remedy certain errors and we have already been penalised more than once this season. Maybe Udinese would have drawn anyway but not in this situation, as the goal was scored by a hand."