Kalinic started the game on the bench but when asked to come on for the last five minutes with his side two goals up, he refused.
Croatian media have reported that the striker complained about a back problem, and this was the reason for his refusal to play.
Croatia won the game 2-0 thanks to an own goal and a Luka Modric penalty.
Next up they face Argentina, who drew with Iceland in their opening game after Lionel Messi missed a penalty.