League leaders Zenit were losing 4-2 at home to visiting Dinamo after Kevin Kuranyi had helped to lead a turnaround following Danny's sixth-minute opener.
Shortly after Alexander Kerzhakov scored Zenit's second, a section of home supporters ran onto the pitch and attempted to attack the visiting players, with the referee forced to call a halt to proceedings and lead the teams off the pitch in the 86th minute.
Villas-Boas also entered the pitch in an effort to stop the fans, one of whom reached Dinamo's Vladimir Granat and landed a punch to the side of his head. The match was abandoned and rescheduled to continue place next week.
After the match, Zenit released an official statement apologising for the incident and condemning those responsible.
"Zenit express extreme regret for what happened at today's match," the club said. "The fans' actions are absolutely unacceptable.
"The police and the club are currently investigating what happened, and we wish justice to be served. We apologise to all the players, coaches and fans for what happened.
"We are very sorry for what happened to Vladimir Granat, and repeat that such fan behaviour is completely unacceptable."
Zenit midfielder Anatoliy Tymoshchuk added that the referee had no choice but to abandon the game as supporters began to flood onto the pitch.
"There are rules. The referee made the right decision," he told reporters. "What happened, happened."