She had been scheduled to ride in the multi-event omnium, in which she won gold at the 2012 and 2016 Olympics, but Katie Archibald will now take her place.
"I am absolutely gutted to announce that I won't be riding in the omnium at the world championships today," Kenny, who is married to British sprinter Jason Kenny and gave birth to a son in 2017, said in a statement.
"I haven't been feeling right all week for reasons we're not sure of, but we do know my performances in the team pursuit over the last two days have been well off where I have been in training over the last two weeks."
Kenny's withdrawal is a blow to the British team who were beaten by Australia in both team pursuit finals on Thursday.
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Stephen Park, performance director for British Cycling, said he expected her to be firing on all cylinders soon.
"I know Laura is disappointed she can no longer compete out here in Poland, but it is the right decision for both herself and her team mates," he said.
"I have no doubt she will soon be back to her winning ways and, in the meantime, Katie deserves credit for stepping in and I'm confident she will put in a strong performance."
(Reporting by Martyn Herman; Editing by Christian Radnedge)
