The 26-year-old Dnipro defender was a regular during Croatia's qualifying campaign but has been ruled out of the finals after collecting an injury towards the end of the season.
Strinic was called up by Kovac with the hope he would recover in time to travel to Brazil.
However, the national coach revealed on Thursday that Strinic had not progressed enough to be considered.
"Additional medical exams showed that Strinic has ruptured his hamstring muscle," said Kovac. "I feel sorry for him but he will not travel with us to the preparation camp in Austria and therefore will not be among the candidates for the World Cup.
"Unfortunately, we don't have enough time to wait for him to get fit again
"I don't want to make a noise about it. Yes, it is a problem but we will find a solution among the players that we have on the provisional list.
"We have players that can cover that position and players that have done it in the past."
Strinic has 32 caps for Croatia and was an ever-present during their last tournament appearance at the 2012 European Championship.
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