The warrant states 20-year-old Brianna Ashanti Lofton "confessed to the act."
Lofton is facing charges of felony child abuse, contributing to delinquency and possession of marijuana.
A version of the video that received more than 1 million views was posted by a user who urged the mother's arrest.
The 10-second video showed the hand of an adult off-screen holding what appeared to be a cigarillo to the child's lips. The child then appeared to inhale and puff smoke.
Allan Maldonado, 18, is also facing charges of contributing to the delinquency of a child and possession of a Schedule VI controlled substance.