The AC Milan player was left on the bench for the Croats’ Group D opener.
It was the fourth successive international fixture where he had been left on the bench.
But asked to come on in the 85th minute, Kalinic reportedly complained of a back problem and refused to play, something which didn’t convince his manager.
His exit means Croatia have just Mario Mandzukic left within their squad as an out-and-out No.9.
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.