Many performances were pre-taped, and none were in front of significant crowds.
The Grammys had been scheduled this year to return to its traditional home next door, the Crypto.com Arena, formerly the Staple Center.
"We look forward to celebrating Music's Biggest Night on a future date, which will be announced soon," the academy statement said.
Finding that date could be complicated, with two professional basketball teams and a hockey team occupying the arena. The Recording Academy made no mention of a possible venue change in its statement.
The move was announced around the same time the Sundance Film Festival cancelled its in-person programming set to begin on Jan. 20 and shifted to an online format.
The multitalented Jon Batiste is the leading nominee for this year's honours, grabbing 11 nods in a variety of genres including R&B, jazz, American roots music, classical and music video.
Justin Bieber, Doja Cat and H.E.R. are tied for the second-most nominations with eight apiece.
The Grammys' move could be the beginning of another round of award-show rescheduling, with the Screen Actors Guild Awards planned for February and the Academy Awards for March.