The incident happened on Edgewood Court in Hempstead on April 13 at 4:00 p.m.
Investigators found Natashia Reed, her 3-year-old boy and 5-month-old baby girl inside the apartment during the fire.
All three went to Nassau University Medical Center for treatment.
The baby girl suffered second degree burns. The boy was not injured.
Reed remains in the hospital, and that's where police arrested her on Wednesday.
Reed originally told investigators the fire started while she was cooking, but police say the evidence wasn't consistent with a grease fire.
An officer with child protective services following up on the case put two and two together.
Investigators say Reed used her kitchen range to ignite paper, which she then threw at the infant and her four year old son, who wasn't hurt.
The baby spent four days at the hospital, but is now recovering with family.
Reed is charged with Arson 2nd Degree, Assault 2nd Degree and Reckless Endangerment 1st Degree.
She received a bedside arraignment at the Nassau University Medical Center, where she is listed in critical but stable condition.