Kenny, a two-time Olympic champion in the event, said after Britain took silver behind Australia in Thursday's team pursuit final that she had been not been able to produce her best form for unknown reasons this week.
"I am absolutely gutted to announce that I won't be riding in the omnium at the world championships today," Kenny wrote on Instagram.
"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.
"I would have given the omnium my best shot and I really wanted to do it but with the depth of the squad it was decided that it was better that I didn't compete and give someone else the opportunity.
"I agree with the decision and I think Katie will do a brilliant job. I wish her, and all my team mates, the best of luck for the rest of the competition."
Her withdrawal brings to an end a frustrating week for both Kennys in Pruszkow.
Kenny and Archibald rode alongside Ellie Dickinson and Elinor Barker in the women's team pursuit on Thursday night but trailed Australia throughout the final, eventually losing by just two tenths of a second.
Kenny said "I feel like I've let the girls down" after the final, having peeled off the group with 1,250 metres to go, just as she did in qualifying.
Husband Jason had no joy at all, with the men's team sprint squad missing out on the medal rounds in their event on Wednesday.
But in Archibald Britain have a very capable stand-in for the omnium. The 24-year-old, who is also slated to ride in the Madison alongside Neah Evans on Saturday, won omnium gold at the Hong Kong world championships two years ago.
British Cycling performance director Stephen Park said: "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.
"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 in today's omnium event."
