Gavi, 19, will undergo surgery next week and won't play for Barça again this season, with his participation in Euro 2024 next summer also effectively ruled out.
"It is a huge loss for us," Xavi said ahead of Barça's LaLiga game away at Rayo Vallecano on Saturday.
"You can't replace him; the heart, passion and courage he plays with. We have to try and find solutions without him, but it's difficult.
"Rayo is the type of game where we need Gavi's mentality and quality. It will be intense. Vallecas is always a difficult place to go for us."
Sources told ESPN that Barça were "angry" with the Spanish Football Federation (RFEF) after playing Gavi in back-to-back games during the international break despite having already qualified for Euro 2024.
However, Xavi said he had no problem with Spain coach Luis de la Fuente's management of the situation and proposed a change to the way international football is shoe-horned into the calendar.
"I think the injury is related to the schedule," the Barça boss said. "At Gavi's age, with the amount of minutes and games he has had... Sometimes [injuries] can just be unfortunate as well.
"FIFA are looking at the possibility of having eight or nine months with your club, going away with your national teams for up to two months and then having time off. It would avoid so much travelling.
"[Ronald] Araujo and Raphinha are just coming back from 14-hour flights. They haven't trained and tomorrow we have a game. There are players -- from Africa, South America and Asia -- that have to travel too much."
Frenkie de Jong is fit to return to action, though, following a two-month injury layoff, with Sergi Roberto also back in training and expected to be available for Tuesday's Champions League game against Porto.