Welcoming back French defender Philippe Mexes after a three-game ban, Milan missed the chance to go up the table despite a third match undefeated.
In a tight match, Keisuke Honda had a chance for Milan in the 48th minute, while there was almost an own goal after Chievo's Alex saw a shot deflected off a defender past Milan goalkeeper Diego Lopez.
In other matches this weekend, Argentina striker Gonzalo Higuain returns from a one-match suspension as Napoli look to boost their Champions League qualifying bid away to Torino on Sunday, while struggling title hopefuls Roma host runaway leaders Juventus on Monday.