The 30-year-old, who is on loan from Manchester City, suffered the injury during Everton's 1-0 Premier League win against Aston Villa last month.
Grealish made 22 appearances in all competitions for Everton this season, scoring twice and providing six assists, and his form had prompted suggestions he could earn a recall to the national side.
"Didn't want the season to end like this but that's football, gutted," he posted on social media.
"Surgery done and now all focus on getting back fit. I know for sure I will come back fitter, stronger and better than before."
Grealish, who won three Premier League titles, the Champions League and the FA Cup with City, made his last appearance for England in October 2024 under caretaker manager Lee Carsley.
The World Cup will take place from June 11 to July 19 in Canada, Mexico, and the United States.