After helping Serbia to 3-0 wins over Kazakhstan and Australia which sealed their place in the final, Ivanovic suffered the injury in practise and the team has been forced to withdraw from Saturday's final, to be replaced by Belgium.
It is a blow for Novak Djokovic who has been in fantastic form all week, winning all of his singles rubbers without dropping a set. Djokovic had been hoping to lift a second team title for Serbia after winning the Davis Cup last month.
Ivanovic has withdrawn from next week's Sydney International but is fairly confident she will be fit for Melbourne.
"I am positive I will be fit in 10 days,” she said. “This morning, I was playing some points and on one serve I felt a sharp pain and I couldn't even hit or move after that. At this moment in time (my chances) are still very good because I stopped in time.”
"It is very frustrating because it has been the case for a long time, always little bits and pieces. It's not a huge deal but it's stupid and a bad timing. I have to stay positive, at least I have a week before the Open rather than this time next week."