Several other presidential candidates, including Trump, have featured on the programme during previous election campaigns.
Trump's appearance came in 2015, when he hosted the show.
However, going on the programme so close to election day is unusual.
Brendan Carr, a Republican member of the Federal Communications Commission media regulatory agency's five-person board, slammed the move as "a clear and blatant effort to evade" its equal time rule.
The federal policy requires US broadcasters to treat political candidates equally in terms of air time, and Mr Carr wrote on X that its purpose is "to avoid exactly this type of biased and partisan conduct - a licensed broadcaster using the public airwaves to exert its influence for one candidate on the eve of an election".
Asked about the surprise appearance on Fox News, Trump's son Eric said mainstream media has been against his father "from day one".
"I mean, just no one, no one trusts most of those mainstream channels," he said. "I'm not sure if the Saturday Night Live stuff is going to ultimately matter. I think it's my father's work ethic [is] going to matter."
Harris briefly stepped away from her campaign in the battleground states to make Saturday's surprise trip to New York for the broadcast.
She arrived on Air Force Two, at LaGuardia Airport, following early evening campaigning in Charlotte, North Carolina.
Harris was scheduled to head to Detroit but aides said she'd be making an unscheduled stop once she was in the air.
Her appearance wasn't announced beforehand and was only confirmed by an official moments before it began.
Polls show the two presidential candidates are locked in a tight race in seven key swing states.
Both Harris and Trump are preparing a blitz of these battleground states in the final days of the campaign.
