The actress had been in contention to star in Ned Fox Is My Manny as a single mother who enlists her brother's help to raise her child.
A source has told Deadline that Elliott has now departed the sitcom and will continue as a castmember on SNL.
It is not yet known who will be replacing Elliott in Ned Fox Is My Manny.
Elliott joined Saturday Night Live in 2008 and has impressed viewers with her impressions of Angelina Jolie, Zooey Deschanel and Khloe Kardashian.
Her father Chris Elliott was also a castmember of SNL from 1994 to 1995 and her grandfather Bob Elliott appeared on the late-night series as a guest in the 1970s.
Saturday Night Live airs at 11.30/10.30c on NBC.
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Watch Abby Elliott in Saturday Night Live's 'Bad News' sketch below: