Barca confirmed on Monday that Fati's recovery is "following a very satisfactory course".
Fati scored five goals and provided two assists in 10 games in all competitions this season before suffering his injury against Real Betis.
The Spain international is expected to be back in contention to play in March, meaning he will likely miss at least the first leg of Barca's Champions League last-16 encounter with Paris Saint-Germain, which takes place on February 16.
Barca lost two of their first three LaLiga games after Fati's injury but have since won four and drawn twice in six top-flight fixtures.
They sit fifth in the table, 10 points behind leaders Atletico Madrid, having played a game more.