Dzeko lasted just four minutes as a second-half substitute at QPR in the Premier League on Saturday before picking up an apparent injury and making way for Frank Lampard.
The striker still flew out to his homeland to report for duty ahead of his country's Euro 2016 qualifier away to Israel on Sunday.
But he has been diagnosed with a ruptured adductor in his right thigh - an injury that generally requires a recovery period of anything between two to six weeks.
Team doctor Reuf Karaberg told the Bosnian FA's website: "The injury is very serious and requires some recovery time, which, unfortunately, is in conflict with the possibility of a rapid return to the field."
Safet Susic has already been shorn of Stuttgart striker Vedad Ibisevic, leaving him with no recognised spearheads in his squad, and the Bosnia coach has written off his side's hopes of securing all three points at the weekend,
"If Dzeko can't play we will be resigned to playing for a draw against Israel because we have no hope of winning without him," Susic told Bosnia’s FENA news agency.
