Ante Cacic's men sit four behind leaders Italy and two back from second-placed Norway in third position in Group H. They will be looking for six points from their final two matches in order to avoid a potential play-off tie.
Mandzukic, 29, who has scored once in eight appearances during the qualification campaign, will not be able to assist his nation after the Croatian Football Federation (HNS) confirmed his injury.
"Unfortunately, he has picked up a hamstring injury. Today [Wednesday], we have reviewed it and conducted an ultrasound and according to the finding he will not be able to play in these two games," explained national team doctor Boris Nemec in a statement on the official HNS website.
"I think he needs another two weeks to begin full training, with a high percentage of certainty that there will not be a relapse.
"Of course, he was not happy with such news, but his health has to come first."
Croatia host Bulgaria in their penultimate fixture on Saturday before travelling to Malta for their final group match three days later.