Jankovic reached the Australian Open semi-finals last year
World number one Jelena Jankovic's Australian Open plans were hit after she pulled out of the Hong Kong World Team Challenge with flu.
The Serb, lacking match practice ahead of the year's first Grand Slam on 19 January, said: "I have been feeling weak and sick for a couple of days.
"I really have been trying my best to go on the court but I feel slow."
Venus Williams beat Vera Zvonareva 6-2 6-2 to give Team Americas victory over Russia in the exhibition event final.
Wimbledon champion Venus, who had beaten Jankovic 6-2 6-2 in the Serb's only singles match in the tournament on Thursday, also beat Anna Chakvetadze in straight sets on Friday.
I'm on medication and I have to rest and try to recover as fast as possible
"It's definitely a great way to start the year with wins against such talented players," said Venus, who later won her doubles match to secure a 4-1 win for Team Americas.
"This is the perfect way for me to prepare for the Australian Open."
But while the world number six goes into Melbourne event in great shape, Jankovic, who is still seeking to win her first Grand Slam crown, faces a battle to get her game into shape.
"Nobody likes to be sick and and now I'm on medication and I have to rest and try to recover as fast as possible," said Jankovic, who has played only one singles and one doubles match this year.
"It's disappointing because I take care to try to play some matches and try to work on my game and get ready for the big Grand Slams but sometimes it's bad luck. What can I do?"
With the final tied at 1-1 after Friday's matches, Argentina's Gisela Dulko rallied to beat Chakvetadze 3-6 6-4 6-4 to give Team Americas the lead in the best-of-five final.
Venus made it 3-1 before teaming up with Coco Vandeweghe to beat Chakvetadze and Alexandra Panova 6-4 6-1 in the doubles.
Asia Pacific, who lead 2-0 overnight, beat Europe 3-0 in the play-off between the beaten semi-finalists.