Sunday's crucial Premier League clash with Dinamo Moscow saw fans invade the pitch in the 87nd minute as title-chasing Zenit trailed 4-2.
With supporters spilling onto the pitch, one fan appeared to direct a punch at Dinamo's Vladimir Granat.
Zenit immediately apologised for the incident and head coach Andre Villas-Boas admitted on Tuesday he expected heavy sanctions to be passed down.
Those arrived on Wednesday. As well as the stadium ban, Zenit must play their following three games at Petrovsky Stadium with the stand from which the fans emerged closed and pay a one million ruble fine.
Zenit general director Maxim Mitrofanov expressed disappointed at the ruling, but insisted the club were working with local police to ensure there would be no repeat in the future.
Mitrofanov also claimed the club would attempt to force the fans responsible for the sanction to pay the fine between them.
"The CDC's (Control and Disciplinary Committee) decision is harsh, but it's important that there will still be football in St. Petersburg next season," he said. "Yes, unfortunately we'll play two matches behind closed doors, but after that, real fans will be able to watch the team play.
"As for the fans who were in sectors 12, 13, 14 and 15 at Petrovsky Stadium, these sanctions are only a part of the measures that will be taken against them in accordance with the CDC's decision.
"Right now the club, in cooperation with the police and the St. Petersburg city administration, has developed a set of measures, both legal and organisational in character, designed to never again allow unlawful and illegal actions of fans in our stadium.
"As for the fine given to the club, it will be partially charged to the hooligan who hit the Dinamo player, and to the other spectators who ran onto the pitch - after conducting the corresponding investigation and determining these individuals' personal identity."
