Uncertainty around the Omicron variant means going ahead "simply contains too many risks", according to a statement from the Recording Academy and CBS.
The event, which is regarded as music's biggest night, was scheduled to take place on 31 January in Los Angeles.
It will happen on a future date to be announced soon, organisers said.
The health and safety of the music community, the live audience and hundreds of employees remained their top priority, they added.