A group of fans of the club from the southern city of Porto Alegre chanted insults and made monkey noises standing behind Aranha's goal.
One young female supporter clearly seen yelling "macaco" (monkey) at the shot-stopper was suspended from her job while her behavior sparked a storm of outrage on social media.
A spokesman told AFP the tribunal made its decision unanimously though Gremio chairman Fabio Koff appealed on behalf of the four-times Cup winners now coached by former Brazil coach Luiz Felipe Scolari.
Pending a final ruling in the case the second leg of the match is suspended.
Santos won the first match 2-0.
Incidents of racism have marred games in several countries but the punishment usually takes the form of a fine or having to play matches behind closed doors.
Last May, FIFA president Sepp Blatter urged harsher penalties, including expulsion from cups and deduction of league points, to be imposed on clubs whose fans indulge in racist abuse.
Six seasons ago, French side Paris Saint German were expelled from the league cup by the French game's disciplinary commission after some fans held aloft a banner at Stade de France insulting people hailing from around Lens, their opponents.
The Aranha racism case was only the latest in a series in Brazil in recent months.
Gremio condemned the fans involved but the incident was the second this year involving the club's fans -- the first earned the club a fine of $35,000.
Shocked at the racism -- in one instance a black referee had bananas thrown at his car -- Brazil's government promised before the World Cup to crack down.
Last April, Brazil starlet Neymar publicly waded into the debate by posting a picture of himself on social media eating a banana after Barcelona teammate and compatriot Daniel Alves picked up one which had been thrown on the pitch near him during a game in Spain.
Neymar then launched a campaign using the hashtag somos todos macacos (we are all monkeys).
