The celebration, common all over South America, involves supporters behind the goal charging down the terraces en masse towards the front.
Club president Fabio Koff said the club would install seats in the terraces behind the goal at the recently-opened Arena Gremio to curb the fans' enthusiasm.
"We have to face the facts after what happened. There's no alternative but to install seats," club president Fabio Koff told Brazilian media.
"We don't want to turn this into an elitist stadium but there have been some excesses, which we can bring under control."
The fence at the bottom of the terrace gave way after fans stormed downwards to celebrate a goal in the Libertadores Cup match against Ecuadorean side Liga de Quito.
Photographs and videos posted on YouTube showed that several fans fell about one metre into the ditch which separates the pitch from the terraces.
The Arena Gremio is one of Brazil's most modern stadiums although it will not be used as a 2014 World Cup venue.