The Omicron variant is all over the Big Apple, and a new spike in cases has got everyone spooked -- including the folks over at 'SNL' ... who will go without a live audience tonight.

"Saturday Night Live" honchos made the announcement Saturday, just hours before showtime ... with Paul Rudd slated to step in as host, and Charli XCX as musical guest. There were rumors they may nix the show entirely, but they met somewhere in the middle.

The official 'SNL' IG page posted a new message, which reads ... "Due to the recent spike in the Omicron variant and out of an abundance of caution, there will be no live audience for tonight's taping of 'Saturday Night Live' and the show will have limited cast and crew."

The statement goes on to say their show continues to follow all government safety protocols, with rigorous testing in place.

The limited cast and crew line is curious in the wake of a report claiming 4 'SNL' members actually caught the 'rona -- which a production source confirms to TMZ. There were also rumblings that 3 others called in sick out of fear, but we're told that's not accurate.

In any case, it's clear they're working without at least a handful of people tonight -- at this point, it's unclear who's out sick ... or if Paul or Charli are expected to show at this point.

PR was featured in a promo they just put up earlier today, so presumably ... he might still be available. Of course, it's a huge deal -- as this is the last show of the year before they go on a little hiatus ... so it'll be interesting to see how they handle the last-minute changes.

We've reached out to a rep for 'SNL' ... so far, no word back.