Vucinic, 29, was berated during the session after missing an easy chance in front of goal, and the Montenegro international did not take kindly to the abuse.
During the middle of training in Chatillon, Vucinic reportedly walked over to the fan and began a verbal altercation with him.
Juventus manager Antonio Conte was working with other players at the time but goalkeeper Marco Storari, midfielder Thiago Motta and team officials calmed the simmering tension by removing Vucinic from the argument.
The forward is reported to have apologised to the fan responsible later in the training session.
Vucinic, who has been recently linked with a switch to Manchester United, signed for Juventus in 2011 following a successful five-year spell at Roma.
His on-edge mood is no surprise given Juventus' recent signings of strikers Fernando Llorente and Carlos Tevez, with Vucinic's future potentially under threat at the Serie A champions.