Olic, who has agreed to join Wolfsburg from Bayern Munich this summer, sustained the injury in a 1-1 friendly draw against Norway on Sunday.
Croatia were initially hopeful that the 32-year-old would recover from the problem in time to face Spain, Italy and Ireland in Poland.
However, tests have revealed a rupture to a thigh muscle and it is expected Olic will be sidelined for between four and six weeks.
"Medical tests surprisingly showed a rupture and partial tear of the muscle and his recovery is going to take from four to six weeks," said Croatia team doctor, Zoran Bahtijarevic.
Croatia have called up Dnipro striker Nikola Kalinic as a replacement. He represented Blackburn between 2009 and 2011, scoring seven goals in 44 Premier League games.
Croatia can also call upon Everton striker Nikica Jelavic to partner Eduardo da Silva in attack.
Olic has scored 15 goals in 78 caps for the country.