A legislator from Shalimar Bagh, Kumari was unhappy with party nominating Anvika Mittal for a by-pollcandidate.
Kumari's resignation has been submitted to Delhi Chief Minister and AAP Chief Arvind Kejriwal.
The norm is to send the resignation to the Speaker.
There was no official word from AAP on Kumari's resignation but a close aide of her said "yes, she has submitted her resignation to the Delhi CM."
After winning five seats in the MCD by-poll, which was below the party's expectations, AAP had said that it will introspect over the results and also ask the MLAs the reasons for the defeat.