Soyuncu picked up the injury while on international duty with Turkey last week.
The 24-year-old was one of three key players missing for Leicester City on their return to Premier League action on Sunday when they lost 1-0 to Aston Villa at home.
Jamie Vardy also missed the game with a calf problem while Wilfried Ndidi has already been ruled out for three months with an abductor injury. Right-back Ricardo Pereira has been out since March with a knee problem.
Soyuncu played in Leicester first four league games of the season, with the Foxes winning three of those games and his absence will be of huge concern to manager Brendan Rodgers.
'(Caglar) Soyuncu is more serious in terms of the muscle is right off the bone,' Rodgers said.
'So he could be out for three months, which is an absolute shame. He did it training with the Turkish national team.
'He'll be a big miss and adds to the other boys who are out.'
Leicester City will open their Europa League campaign with a home game against Ukrainian side Zorya Luhansk on Thursday before travelling to the Emirates Stadium to face Arsenal in the Premier League on Sunday.
