Kulhavy came down with the flu on Sunday after racing the Velká Bíte - Brno road race on Saturday.
"Even while racing on Saturday, I was not feeling too well, and I was cold," said Kulhavy on his website. "On Sunday, then came the fever and the intestinal problems. I have therefore decided, after consultation with the team, to pass on the first World Cup."
"My actual form after a long break, combined with my condition due to the flu, meant I would probably not have had a good race. I would prefer to get everything together for the second round in Australia."
Kulhavy is just coming back to training and racing after fracturing his kneecap.
Round 2 of the World CUp will happen in Cairns later this month.
"Although I now feel a little better, I do not feel I can get on a plane in this situation and travel to Africa," he said.
In Saturday's 138km road race in the Czech Republic, Kulhavy finished with the main field.
"The race was a bit of a shock. I wasn't doing anything extra in the race, but in in the end, when we rode up the hill, I lacked strength."