"The club considers the reasons outlined in the referee’s report inadmissible and has therefore appealed to the competition committee," Barca said on their website on Tuesday.
According to the report filed by referee Carlos Del Cerro Grande, Suarez and Rakitic were booked for catching an opponent with an arm while Vermaelen was cautioned for tripping one of the Bilbao players.
Barca's next outing is their first home league game of the campaign against Malaga on Saturday.
Coach Luis Enrique looks likely to have Neymar available after he returned to training earlier than expected on Monday.
The Brazil forward has been suffering from mumps, depriving Barca of one-third of their lethal attack that includes fellow South Americans Suarez and Lionel Messi.
The trio scored a Spanish record 122 goals in all competitions last term as Barca swept to a treble of Champions League, La Liga and King's Cup titles.
(Reporting by Iain Rogers, editing by Tony Jimenez)
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