"I had the first therapy today and I've been told that I will be out of action for at least a month," Pjanic told the Bosnian weekly Slobodna Bosna on Tuesday after limping off in Roma's 3-1 win over Serie A rivals Genoa on Sunday.
Pjanic can at least take consolation from the doctor's diagnosis that he will not have to undergo surgery and said he would be in the Zenica stadium to cheer on group leaders Bosnia.
"I have mixed feelings. I am so happy because the injury is not as serious as it first looked but then again I am also very sad because I will not be able to play," he said.
"Still, I believe in Bosnia's victory though it seems we always have to do it the hard way."
Bosnia, who are aiming to qualify for their first major tournament as an independent nation, share top spot in the group with Greece as both sides have 10 points from four games.