Inter Milan winger Perisic scored in the 3-1 win over Scotland on Tuesday night, which secured a place in the last 16 as runners-up to England in Group D.
The Croatian Football Federation said all of the other players, staff and members of the delegation had tested negative.
A statement on the CFF’s website read: “During Saturday evening, Croatian Football Federation received the results of regular testing for the SARS-CoV-2 virus, which showed that player Ivan Perisic has tested positive for novel coronavirus.
“Medical staff isolated Ivan from the other members of the national team and immediately and thoroughly informed competent epidemiological authorities about the situation, providing evidence of complying with all the necessary measures aimed at protection against the spread of coronavirus.
“Perisic will spend 10 days in self-isolation and during that period will not participate at the matches of the Croatian national team.
“All other players, staff and delegation members tested negative.
“National team will be travelling from Pula on Sunday 27 June with a charter flight to Copenhagen, where it plays a round-of-16 match of the UEFA EURO 2020 against Spain on Monday.”