Barca can appeal and may get the sanction reduced but if that fails the Spain international will miss the Spanish and European champions' opening four La Liga matches, including Sunday's trip to play Bilbao and the game at Atletico Madrid on Sept. 12.
Pique apologised via his Twitter account on Tuesday and denied using insulting language.
With Barca attempting to overturn a 4-0 deficit from the first leg and leading 1-0 on the night, he was shown a straight red card 10 minutes into the second half at the Nou Camp.
Referee Carlos Velasco Carballo acted after Pique strode angrily up to the linesman and yelled in his face.
Bilbao levelled the score at 1-1 on the night 16 minutes from time to secure a 5-1 aggregate success.
A Barca spokesman said the club had not yet decided whether to lodge an appeal.
(Reporting by Iain Rogers, editing by Sudipto Ganguly)
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