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Arruabarrena's departure follows a 1-0 loss at Racing Club on Sunday, with his team taking just seven points from their first five games and suffering a 4-0 defeat to San Lorenzo
The 40-year-old who was appointed in 2014, guided Boca to Primera Division and Copa Argentina glory last season, but has been unable to replicate that this year.
"They are sad and difficult days where you have to make decisions thinking about what is best for the club," Boca president Daniel Angelici said.
"We took the decision to terminate the contract with the coach and wish him luck
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"Professionally, he has given a lot to Boca and is a person who will leave a mark."
Arruabarrena had been under pressure since Boca - captained by Carlos Tevez - opened the season with four consecutive defeats, two of those coming against arch-rivals River Plate, in the Torneos de Verano - a pre-season tournament but considered an important competition.
Former Palermo coach Guillermo Barros Schelotto is the frontrunner to take up the vacant position, while Jorge Sampaoli has also been touted as a potential candidate.
Barros Schelotto resigned from his role at the Serie A club after UEFA refused to hand him a coaching badge, while Sampaoli is without a job after leaving his position with Chile.