Gavi is an effective player for Barcelona and Xavi was surely counting on this player for the rest of this season. I think Barcelona is even right to start blaming Luis de la Fuente for it because the game against Georgia was not an important game for them to let Gavi play in this match.
Regardless of that, Barcelona can have 30 days to hire another player to take Gavi's place in the team. They just need to prove Gavi is out for four months or more which is not hard and there won't be any financial issues for Barcelona about hiring the new player.
International competitions always come with injuries. Gavi wasn't lucky and like Eduardo Camavinga or Vinicius Junior, he got an even worse injury in the knee and will be absent for the remaining period.
I think FIFA give money to the clubs in case of injuries happening while their players are playing with them internationally. Yet, for Barcelona, losing Gavi will make the team more unstable and they have to pick a close substitute. We all know that Barcelona don't spend much money so..good luck finding someone who could replace him perfectly.