Kalinic, who played for Blackburn Rovers between 2009 and 2011, was starting his fourth worldwide in a row on the bench and complained of the same problem in the friendly loss to Brazil.
Reports emerged earlier on Monday that Kalinic had refused to come off the bench during his country's opening 2-0 win over Nigeria in Group D, citing his back complaint.
Speaking in the wake of Saturday's win, Dalic told reporters that the team had finished the game without injuries but "with a problem".
"During the Nigeria match, Kalinic was warming-up and should have come in the second half".
And when manager Zlatko Dalic asked him to come on in the 85th minute, he straight up refused.
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Volkswagen, which last week agreed to pay a fine of €1 billion ($1.2 billion) imposed by German prosecutors, confirmed the arrest. The scandal erupted three years ago, when it emerged that cars had been fitted with devices created to cheat emissions tests.
Dalic did not answer any further questions or go into the matter any further.
Croatia are back in action against Argentina in Nizhny Novgorod on Thursday.
It seems the decision was later taken to axe the AC Milan forward with Kalinic believed to be taking the first flight back home from Russian Federation this week.
After making a positive start to their World Cup campaign, Kalinic's departure will no doubt impact Croatia's preparations, as the 30-year-old was one of only two out-and-out strikers, alongside the man he was suppose to replace - Mandzukic.
"I need players who are fit and ready to play and Kalinic isn't", he explained in his pre-match press conference.