Atletico Mineiro, the home team, was fined about $10,000.
Cruzeiro said it will appeal.
"This is a police case," Cruzeiro club director Alexandre Mattos said. "Authorities need to prosecute those involved in the incident. We did all that we could have done."
Seeking its first national title since 2003, Cruzeiro has a nine-point lead over second-place Gremio with eight rounds left in the Brazilian league. The club will still be able to host the match against Criciuma at the Mineirao Stadium on Saturday. It's possible the suspension is served against Gremio, depending on the length of the appeal process.
Because of the tribunal's suspension, Sao Paulo will not be able to play home matches until the end of this year's Brazilian league. The team is 10th in the 20-team standings. It plays at Internacional on Sunday.
The tribunal also fined the six-time champion about $40,000 for the problems in the match against Corinthians at the Morumbi Stadium, when police used batons to keep Sao Paulo supporters from invading the rival fan section. Television images showed bloodied fans throwing punches at officers and some fans with small children trying to flee the chaos.
After the match, supporters from both teams clashed at a major avenue. A bus carrying Sao Paulo fans had nearly all of its windows destroyed and police seized several iron bars and rocks used in the confrontation. Authorities detained at least 30 people involved in the clash, including several women.
The tribunal fined club world champion Corinthians about $10,000 because some of its fans also were involved in the incidents at the Morumbi.
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