A friendly between the sides last Thursday was abandoned after 26 minutes when Boateng responded to abuse by suddenly picking the ball up and kicking it towards the stand behind him.
The Ghana midfielder then tore off his shirt and walked off the pitch, followed by the rest of the Milan side.
The Lega Pro, the governing body for Italian football's third and fourth tiers, yesterday released the findings of their sporting tribunal, noting that in October the club had been fined €5000 (£4000) over "similar incidents".
The verdict read: "[The Lega Pro] will impose on the club Aurora Pro Patria the sanction of the obligation to play a league match behind closed doors, with immediate effect, with the caveat that further breach will be evaluated as an occurrence of multiple violations, for the purposes of the subsequent sanction."
In explaining the sanctions, the governing body wrote that the incident was particularly serious as it occurred during a friendly and thus could not be "mitigated" by "competitive tension and competitive spirit".
The statement continued: "The penalty to be imposed for incidents of this nature must be not only punitive but also preventative in order to avoid repetition of the episodes themselves.
"In the current season, the Pro Patria club have already been fined for similar incidents with the fine of €5000 [referring to a verdict released on October 30].
"That previous sanction has been shown to be ineffective by this recidivist behaviour."
The Italian federation president, Giancarlo Abete, whose organisation has long battled racism among fans, said officials could act in the future before players have to.
"If it is necessary to suspend the game, we will do it to stop this phenomenon," he said.