Zinedine Zidane's side produced a toothless attacking performance in drawing at home with Real Betis 0-0 on Saturday, its second scoreless stalemate in three rounds.
Barcelona's sixth league win in a row lifted it back into second place at seven points behind Spanish league leader Atlético Madrid, which has two more games to play.
Fati sustained the injury during the team's La Liga match against Real Betis here on Saturday. The player played for 45 minutes in the match and was then substituted.