Gago limped off the pitch in the final minutes of Boca's 3-1 extra-time defeat to their Argentine rivals in the second leg of the final at Madrid's Bernabeu stadium on Sunday, a result that handed River a 5-3 win on aggregate, reports Xinhua.
"Be strong, Fernando," Boca said in a statement on social media after scans confirmed the 32-year-old's worst fears on Monday.
Most footballers require three to six months to make a full recovery from a torn Achilles tendon.
Former Real Madrid playmaker Gago, who has been capped 61 times for Argentina's national team, has been beset by a long list of injuries throughout his career, including two previous Achilles tendon tears.
--IANS
