Zenit trailed Dinamo 4-2 in an encounter that Villas-Boas' side needed to win to ensure they would head into the final weekend of the season top of the table in a three-way title race with CSKA Moscow and Lokomotiv Moscow.
However, the home fans at the Petrovsky Stadium charged into the area behind the away goal in the 87th minute of the contest.
Referee Sergey Ivanov ordered both teams from the pitch as stewards struggled to contain the crowd, however, tempers flared as they exited the field, with a section of the Zenit fans making their way onto the playing surface.
The incident, which saw one supporter appear to direct a punch at Dinamo defender Vladimir Granat, was quickly condemned by the Saint Petersburg outfit.
And former Tottenham, Chelsea and Porto boss Villas-Boas is anticipating the club to be handed a severe punishment.
"It's really sad that this situation took place in our match," Villas-Boas said. "Things like that shouldn't happen.
"It's not acceptable for fans to come on the pitch during the match, just as it's not acceptable for them to be aggressive towards players.
"There can be no violence or racism in football. Of course, clubs, and particularly our club have to implement serious and smart work with fans.
"Of course, we are awaiting the decision by the CDC (Control and Disciplinary Committee).
"Unfortunately, the stadium can be punished, and in this case, the team will play either without spectators, or at another stadium, and that's bad, because fan support is very important to us."
An official decision regarding the result of the match is yet to be confirmed with just one round of matches to be played in the season.
