All Croatia players, including Besiktas centre back Vida, had returned negative tests on Monday and underwent another routine test on Wednesday morning ahead of the Turkey game, a friendly in Istanbul, with a Nations League match against Sweden scheduled for Saturday.
The experienced Vida started the game as Croatia's captain, giving away a penalty in a combative first half.
Turkey's team management were initially informed of a potentially positive result shortly before the second half of the clash, by which time manager Zlatko Dalic had already brought on Filip Uremovic in place of Vida.
Vida, 31, was immediately isolated from the squad before a retest confirmed his positive result. Croatia said he will spend the next few days in self-isolation in Istanbul, home of his club Besiktas, while the team travel to Stockholm.
Croatia added that another member of their delegation had tested positive but was not in contact with the team or staff.
After Saturday's scheduled visit to Sweden, Croatia are due to face Portugal at home on Tuesday in Group 3 of Nations League A.
