In his 753rd appearance for Barcelona, Messi was sent off for the first time in his club career after clashing with Bilbao’s Asier Villalibre in the second half of extra time.
Bilbao twice came from behind, cancelling out strikes by Antoine Griezmann each time before Inaki Williams scored the decisive winner to hand them a 3-2 victory.
Messi will therefore miss Barcelona’s Copa del Rey game against Cornella on Thursday and their La Liga date will Elche on Sunday.
Ironically, the six-time Ballon d’or winner’s first game back from suspension will also be against Athletic Bilbao in La Liga on January 31.
Before Sunday’s dismissal Messi, had been sent off just twice in his career, both coming while on international duty with Argentina. He was red carded on his debut for the Albiceleste against Hungary in 2005 and at the 2019 Copa America third-place playoff against Chile.
Barcelona intend to appeal against the decision to ban their captain, who has scored 14 goals in 22 appearances this season.