Kalinic had started on the bench for the fourth successive international match but was asked to enter the game by boss Zlatko Dalic with just five minutes to go.
According to Daily Mail, Kalinic complained about a back issue forcing Dalic to turn to Marko Pjaca, who is nominally a wide player, to come on in place of Mario Mandzukic.
However, it is understood Dalic was unconvinced by Kalinic’s claim and was left furious at him after the final whistle.
The decision was taken to axe the AC Milan forward on Monday morning with Kalinic believed to be taking the first flight back home from Russia.
Meanwhile, Dalic has called an emergency press conference and is set to clarify the situation later on Monday.
Croatia’s next game is against Argentina on Thursday.