On January 30, during Gremio's 1-0 win over Liga Deportiva Universitaria, supporters celebrated Elano's goal with a so-called 'avalanche', in which fans collectively rush to the front of the terrace.
The celebration is relatively common in South America, but on this occasion a fence was pulled down and a number of supporters fell into the ditch which separates the pitch from the stands.
The South American Football Confederation (Conmebol) said on its website: "Gremio must close the north side of the stadium where the avalanche took place in the next match.
"Furthermore, the stadium will be automatically closed [for one or more games] if any other similar problem takes place in the next two years."
Gremio will have to pay 35,000 US dollars to the Conmebol.
Gremio's next Libertadores match will see the Porto Alegre side meet Chile's Huachipato in the first round of Group Eight matches.