Andre Villas-Boas' men came into the clash knowing victory would guarantee they entered the final round of Russian Premier League fixtures as leaders.
However, with their side 4-2 down and seemingly on course to lose their grip on first place, home fans charged into the area behind the away goal in the 87th minute of the match.
As stewards struggled to contain the on-rushing crowd, referee Sergey Ivanov ordered both teams from the field.
Tempers flared among the players as they left the pitch, and a section of the Zenit support made their way onto the playing surface.
One fan appeared to direct a punch at Dinamo's Vladimir Granat, and Zenit were quick to condemn the incident.
"Zenit expresses extreme regret for what happened at today's match," said the club's press officer. "The fans' actions are absolutely unacceptable.
"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 behavior is completely unnacceptable.
"The police and the club are currently investigating what happened, and we wish justice to be served."
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