Rice and fellow Olympic medalist Eamon Sullivan today appeared at the Myer store in Brisbane's CBD to promote Davenport underwear.
"I haven't been well since Beijing and it's gotten a lot worse since coming home," the Adelaide Now quoted Rice, as saying.
"Perth is not what I should be doing right now. I really want to go to Perth but I can't until I get better. The doctors said I have the early stages of pneumonia which a lot people probably have," she added.
On Wednesday, Rice and and fellow swimming star Eamon Sullivan were caught up in an extraordinary angry confrontation, which left fans crying and swearing.
The incident happened in Melbourne yesterday as they promoted Davenport clothing - and tempers flared among fans over what the swimmers would and would not autograph.
After queueing hours for an autograph, unsuspecting admirers were told the Olympic medalists would sign only Davenport-branded clothing.