The Serb had a scan on the injury on Friday and the results showed a “significant strain”, according to tournament director Paul McNamee.
With the first grand slam event of the year beginning on Jan. 17, world number 17 Ivanovic now faces a race against time to be fit to play.
“It’s obviously a significant strain,” McNamee told reporters. “She’s pretty upset.”
Ivanovic is now likely to pull out of the event in Sydney next week but McNamee said he did not know whether she would be able to play in Melbourne.
“It probably has implications for her, not just tomorrow (in the Hopman Cup final), but also this month.”
Under the Hopman Cup rules, Serbia will not be allowed to bring in a replacement for the final, so Belgium, who finished second in their group, will advance in their place.