Two Goias players, striker Rafael Moura and midfielder Romerito, were also suspended provisionally for the same length of time, meaning they will miss the team's next seven matches, Brazil's highest disciplinary tribunal said.
Goias were involved in a brawl with radio reporters after their 2-2 draw at Vitoria.
The STJD said that coach Leao and the two players were taken to a police station following the incidents and that television pictures showed Moura knocking a radio reporter over with a punch.
"We cannot allow players, directors and coaches to get involved in behaviour which demoralises Braziian football without applying, from the outset, the corrective measures allowed by the disciplinary code," STJD president Rubens Approbato said on the tribunal's website.
"This is an example which can be used, in the future, by those who may have the idea that they can get away with such acts."
Trouble broke out at the end of the match after Vitoria had snatched an 89th minute equaliser.
Leao, who coached Brazil from 2000 to 2001 and played for them at the 1974 and 1978 World Cups, headed straight for the referee to protest about the goal, claiming it was offside.
Touchline radio reporters attempted to broadcast the conversation, leading to a scuffle involving a number of Goias players.
The reporters are a distinctive feature at Brazilian matches. They interview players on the pitch immediately before or after games, when players are sent off, and also run onto the field when there is a disturbance.
Known for his fiery temper, the 61-year-old Leao is coaching his 17th Brazilian club.
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