"During the Nigeria encounter, Kalinic was warming up and was supposed to come on in the second half," Dalic said in a statement.
"However, he then stated that he wasn't ready to come on due to a back issue. The same thing happened during the Brazil friendly in England, as well as before the practice session on Sunday.
"I have calmly accepted that, and since I need my players fit and ready to play, I have made this decision," he added.
The Croatian Football Federation (HNS) said that Dalic had taken the decision after consultation with his coaching team.
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Dalic declined to answer any questions over the issue.
Kalinic cannot be replaced so Croatia will continue in the tournament with a 22-man squad.
Croatia, who beat Nigeria 2-0 on Saturday, face Argentina on Thursday and finish their Group D campaign against Iceland next week.
Media reports said that Kalinic, who has been unable to break into the starting lineup during the build-up to the tournament, had been asked by Dalic to come on as an 85th-minute substitute against Nigeria.
(Reporting by Simon Evans, editing by Pritha Sarkar and Toby Davis)
