Rice, 21, contracted the illness during her flight from Australia to the national team training camp in Manchester on Tuesday, team officials said.
National head coach Alan Thompson said Rice had a cold and would continue to train in preparation for the world championships, where the Beijing star hopes to add a world title to her three Olympic gold medals from last year's Beijing Games.
"It's nothing major. She hasn't missed a session yet," Thompson told The Australian. "Off the plane she was a little bit under the weather. It's more a runny nose than anything."
Rice has had a chequered preparation for the world titles since taking an extended break after the Olympics last August.
She was troubled by a shoulder injury and other minor illness when she returned to the pool late last year, which put her training behind schedule for the world championships.
Rice has been trying to regain her form since the Australian trials in March, where she won her gold-medal events, the 200m and 400m individual medley, and also qualified to swim the 200m freestyle.
"I really didn't get enough work in for the trials preparation because of injury and sickness so I'm looking forward to just trying to really get into the best shape I possibly can be for Rome," Rice said before she left for Europe.
Rice won the medley double and swam in the women's 4x200m freestyle relay win, all set in world record time, at the Beijing Olympics.
Source: AFP Global Edition