“Brozovic's Inter Milan and Swedish epidemiologists were informed about the positive test,” an HNS statement said.
The player's positive result came two days after defender Domagoj Vida was informed of a positive Covid-19 test after playing the first half of a friendly with Turkey in Istanbul.
Apart from Brozovic, 27, one staff member also tested positive.
They were both isolated from other members of the national team.
After Sweden, Croatia play another Nations League game against Portugal on Tuesday.
Croatia, runners-up at the 2018 World Cup, are third in their Nations League group which also includes France, the team that beat them to the World Cup, Cristiano Ronaldo's Portugal and Sweden.