The Croatian international - who joined Inter on loan from Atletico Madrid this summer - suffered the injury to his knee during Croatia's 6-0 humbling by Spain in the UEFA Nations League, and was forced off after only 20 minutes.
The 26-year-old was asked by Italian outlet Mediaset about his injury following the game, admitting: "I'm fine. I felt a pinch in the knee, but it was a problem I had already had at the World Cup.
“I need to get to the bottom of it, and talk about it with the club and the team doctors.”
The extent of Vrsaljko's injury is currently unknown, but he is unlikely to be risked during his side's upcoming Serie A clash with Parma, in the hope that he will have recovered in time to face Tottenham next week.
The defender was a key part of Croatia's impressive displays at the World Cup this summer. He played almost every minute of the tournament for his side and was hugely impressive on the right side of Croatia's defence.
He has made two appearances for Inter in the Serie A so far this season and has impressed for his new side. The Italian side have the option to purchase Vrsaljko at the end of the season, and may well be keen to do so if he can continue to perform at such a high level.
Danilo D'Ambrosio is likely to be the man to replace Vrsaljko if he fails to recover from his injury. The 30-year-old made 34 appearances for Inter last season, with his impressive versatility proving useful for the Italian giants.