Middleton, averaging 20.4 points, was ruled out Sunday after scoring 21 points the previous night in a win over Miami. The two-time All-Star is missing his fourth game this season.
The Bucks began the day a game behind Brooklyn for the No. 2 seed in the Eastern Conference playoffs. They needed a win over the Bulls plus a loss by the Nets to the Cleveland Cavaliers to clinch the second seed. Otherwise, they would finish third in the East.
Milwaukee had won three straight and eight of nine entering Sunday’s game.
The Bulls held out stars Zach LaVine (right knee tendinitis) and Nikola Vucevic (rest) as well as Daniel Theis (sprained right hip), Tomas Satoransky (sprained left ankle) and Troy Brown Jr. (sprained left ankle).
Chicago was eliminated from contention for the play-in tournament Friday when Washington beat Cleveland.