By Simon Cambers
Former world number one Ivanovic was forced to withdraw from the mixed team event because of a "grade one" stomach strain but still hopes to play in the year's first grand slam event, which begins on Jan 17.
Italy's French Open champion Schiavone quit after a set of her match with France's Kristina Mladenovic because of a groin strain.
The Hopman Cup injury jinx also touched British teenager Laura Robson who needed treatment for a glute muscle strain and pulled out of the subsequent mixed doubles as a precaution.
Serbia had already qualified for the final but Ivanovic's withdrawal meant that they will be replaced by Belgium, led by another former world number one Justine Henin.
They will take on the United States, who reached the final thanks to a 2-1 victory over Britain.
Because of its proximity to the Australian Open, the Hopman Cup is perennially afflicted by withdrawals as players are wary at the first signs of pain or tightness.
In total, seven of the 16 players originally named in the line-up for the mixed team event either pulled out beforehand or suffered injuries during it.
Ivanovic said she was still hoping to be fit to play in Melbourne but confirmed that she will ask for a late start in order to give herself more time to recover, with doctors saying she needs three-to-four days of complete rest.
"It's very frustrating," Ivanovic said. "Hopefully I'll be fine for Melbourne but it's definitely a scare."
"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. I'm positive I will be fit."
Schiavone's groin injury is not expected to keep her out for too long, while Robson is due to have a scan on Saturday.
The injury happened in the first set of her 6-4 6-2 defeat to Bethanie Mattek-Sands but Robson completed the match without too many problems.
She pulled out of the mixed doubles in order to give herself time to prepare for the Australian Open qualifiers, which begin on Wednesday.
"I played very well today," said Murray, who won all three of his singles matches. "It was great preparation playing here last year for the Australian Open and I hope I can go one better this year."
Italy were beaten 3-0 by France, with Nicolas Mahut beating Potito Starace 6-3 7-6 in the only match completed in their tie.
(Editing by Alan Baldwin and John O'Brien)