The decision puts an end to South Korea's hopes of using the Games to engage with the North amid stalled cross-border talks.
In 2018, both sides entered a joint team at the Winter Olympics which led to a series of historic summits.
Pyongyang says it has no cases of the virus but experts say this is unlikely.
The country's health system is thought to be completely inadequate for dealing with the Covid pandemic, the BBC's Tokyo Correspondent Rupert Wingfield-Hayes reports.
The announcement makes North Korea the first major country to skip the delayed 2020 Games because of the pandemic. The event is due to begin on 23 July.
This will be the first time North Korea has missed a Summer Olympics since 1988, when it boycotted the Seoul Games during the Cold War.