The 27-year-old was recently announced as a new castmember along with Nasim Pedrad after female comics Casey Wilson and Michaela Watkins were fired from the long-running programme.
Slate made the on-air mistake in a skit called 'Biker Chick Chat', which also featured guest host Megan Fox, TV Guide reports.
The women in the scene were substituting the word "f**king" with euphemisms "freaking" and "fricking", but one minute into the sketch, Slate said: "You know what? You stood up for yourself, and I f**king love you for that."
The comedienne appeared to have realised the gaff when she paused and puffed out her cheeks after she uttered the word.
The portion of the episode aired at 12:40am on the East Coast, when the Federal Communications Commission does not heavily regulate the airwaves as it would during prime time hours. The West Coast broadcast featured an edited version with the curse word removed.
Neither NBC nor Slate has made any comment on the matter.
It was reported earlier that Fox's boyfriend Brian Austin Green appeared in a scene with the actress during the 35th season premiere.