"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.
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)
