The Olympics were pushed back by a year in March due to the novel coronavirus outbreak. Thursday would have been Day 14 of the Games.
The monument, which was installed seven months ago and stands 15.3m tall (50 ft) and 32.6m wide (107 ft), will be cleaned and undergo a safety inspection before being re-installed.
"Since it will be not on display for (the next) four months, this is kind of sad," Atsushi Yanashimizu, planning director at the Tokyo metropolitan government, told Reuters on Thursday.
When the rings are re-installed in December organisers will hope to have a better idea as to whether the Games can go ahead in Tokyo next year amid continuing concerns about COVID-19.