"He'll be a significant absence for us," Xavi told reporters on Monday. "Frenkie is fundamental to how we play, especially given the great form he was in.
"About the timeframe of his injury, it's going to depend on him really but we will have to assess how he's feeling after the next international break (in October)."
Barcelona visit Real Mallorca later on Tuesday, followed by a home game against Sevilla and a Champions League group stage away fixture against Porto on October 4. They visit Granada in the league on October 8 before the break.
The Dutchman is in serious danger of missing El Clasico, which will take place on October 29.
Xavi said he will have to rotate his squad for upcoming matches, with midfielder Pedri also nursing a thigh injury.
"We will rotate not just for the Champions League, but also for the next LaLiga game," he added. "There will be an average of two or three players rotating every game, that's how we understand we have to prevent injuries."