Uruguayan Football Association president Sebastian Bauza announced the ban after the incident at the end of Wednesday's "clasico" between arch-rivals Penarol and Nacional at the Centenario.
A young man was also still in intensive care after being shot during fighting between the teams' rival hooligan gangs in a street close to the Centenario in Montevideo before kickoff.
"We have agreed (with the Interior ministry) that we have to take decisions and send out signals that there are limits that must be respected," Bauza told a news conference.
"The acts that occurred outside and inside the Centenario stadium must not be repeated," he said at Thursday's announcement of the ban.
Police officers had come onto the pitch to shield the referee from protests by Nacional players after the final whistle in the match, part of a mid-season summer-recess tournament.
Bava's arrest was immediately ordered by Judge Alejandro Guido, who was watching the match on television, in a phone call to the ninth precinct police whose office is beneath the Centenario, Uruguay's biggest stadium.
The goalkeeper, who spent the night in jail, was released on Thursday after making a statement along with witnesses and was reported to have apologised for his actions. He had claimed he lashed out after being hit by police shields and a truncheon.
Penarol will not be able to play the final against Argentine second division side Atletico Tucuman, which had been scheduled for Saturday, due to the ban.
Uruguay is attempting to curb violence in the game with the worst incidents involving the hooligan element among fans of Penarol, winners of the Apertura championship in the first half of the season, and Uruguayan title holders Nacional. (Additonal reporting by Malena Castaldi in Montevideo; Writing by Rex Gowar in London; Editing by John Mehaffey)
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