Gago, a former Argentina and Boca midfielder who took over in October, is the club's third manager in a row to leave without winning a trophy after Jorge Almiron and Diego Martinez.
"This is as far as he goes," Mauricio Serna, a member of Boca's governing council, was quoted as saying by TYC Sports.
"It hasn't been easy because he's a man of the house, but we're here to make decisions. We're very grateful. He did his job in the best way possible."
Boca were not immediately available to comment.
Boca have won only 17 of their 30 matches under Gago and suffered an early exit from the Copa Libertadores with a second-round loss to Peru's Alianza Lima on penalties.
Assistant coach Mariano Herron will take over on an interim basis while Boca look for a new head coach, media reports added.
Boca are top of Group A in the Torneo Apertura, the first half of the Argentine top-flight season 10. They visit Tigre next weekend.