The teenage forward was substituted at half-time in Saturday's contest at Camp Nou, Barca later confirming the damage sustained to his left knee.
Fati is now set to have an operation on Monday, after which Barca said they will release further details about the possible length of his absence.
A club statement read: "The first team player Ansu Fati will undergo surgery [on] Monday for the injury to the meniscus in his left knee by Dr. Ramon Cugat under the supervision of the Club's medical services.
"Once this intervention is completed, a new communication will be provided with information on the result and the approximate time of withdrawal."
Fati is Barca's top scorer in LaLiga so far this term having notched four in seven appearances, while he was also on target in the 5-1 hammering of Ferencvaros in the Champions League.
His form has been a bright point in an inconsistent start Barca have made under Ronald Koeman, who had seen his side fail to win four on the bounce in LaLiga prior to the Betis win.
Only Lionel Messi (48) has attempted more dribbles in LaLiga for Barca in 2020-21than Fati (28), while the club captain is the only Blaugrana player to create more chances (13) than his team-mate's return of nine.
Fati had been called up to the Spain squad for this month's international matches against the Netherlands, Switzerland and Germany, but was replaced by Real Madrid's Marco Asensio.