The 18-year-old was named Japanese Swimmer of the Year last month after her record-breaking exploits in the Jakarta pool.
"I was feeling ill and urgently came home from Australia, underwent testing and the diagnosis was leukaemia," Ikee wrote on Twitter.
"I can't believe it, it's a confusing situation. But with treatment this is a disease that can be cured."
The diagnosis will deprive the world junior 50 metres freestyle, 50m butterfly and 100m butterfly champion of the chance to race at the senior world championships in Gwangju, South Korea later this year.
Ikee, who swam the fastest time in the world in the 100m butterfly and second fastest in the 50m butterfly last year, said she would miss Japan's swimming trials to focus on treatment.
"I am going to take some time off and focus on treatment and as soon as possible I want to show an even stronger Rikako Ikee," she added.
Ikee's coach Jiro Miki held out hope she could compete in Tokyo, saying the "possibility was not zero", Kyodo News Agency reported.
"I'm told we wouldn't have been able to discover the disease in ordinary circumstances," Kyodo quoted Japan Swimming Federation Vice Chairman Koji Ueno as saying at a news conference.
"We were able to find her irregularities because she was swimming. In that sense, we were able to find the disease early."
Only North Korean shooter So Gin Man, who won seven golds and a silver at New Delhi in 1982, has won more titles at one Asian Games than Ikee.
Ikee, whose gold medal haul was the most for a female athlete at a single Asian Games, also picked up two relay silvers to match So's record tally of eight medals.
Winning all six of her gold medals in record times in Jakarta propelled her onto the world stage and made her a major name in Japan.
Coming home sixth in the 100m butterfly at the Rio Games as a 16-year-old, Ikee had been expected to compete for medals at Tokyo 2020 but must now focus on getting healthy before thoughts turn to the summer showpiece in 528 days' time.
After news of Ikee's illness broke, Japanese rugby player Ayumu Goromaru offered words of support on Twitter, telling her to "Strive on," while former Olympic swimmer Hanae Ito said: "Everyone is praying".
(Reporting by Jack Tarrant; additional reporting by Chris Gallagher, editing by Peter Rutherford)
