Vlasic, who played no part in Croatia's opening 3-0 Group B defeat to Spain on Saturday, will leave the camp ahead of their second game against Albania on Wednesday.
"I'm extremely sorry that this new injury will prevent me from helping the team. I've done everything possible to be ready, and I'd like to thank the head coach and the coaching staff for the opportunity. I believe in this team and I'm sure they will succeed - I'll be their biggest fan!" Vlasic said in a Croatian FA statement on X.
The injury is a blow for Croatia, whose hopes of making it out of a tough group were already damaged following their comprehensive defeat to Spain.
With Italy still to come in their final group match, anything less than three points against Albania will leave Zlatko Dalic's side, who reached the World Cup final in 2018 and the last four in Qatar two years ago, facing the prospect of an early exit.
"Nikola invested a lot of effort to help the team at the EURO 2024, and he is an integral part of the squad. Unfortunately, this second injury happened, and I can only thank him for everything he's done here," said Dalic.
