Yu Fen Wang, 52, is charged with five counts of attempted murder.
A 13-day-old girl and a 33-day-old girl both suffered stab wounds to their torsos, while a 22-day-old girl has cuts on her chin, ear, and lip.
The victims were found inside the center just after 3:30 a.m. The Mei Xin Care Incorporated was unlicensed, according to authorities.
The infants were taken to local hospitals in critical but stable condition.
A 63-year-old female daycare worker was also stabbed several times in the torso, and police say a 31-year-old father of one of the babies heard her screams, intervened and was stabbed in the legs.
The female victim is in surgery for her injuries at New York-Presbyterian/Queens.
"We pray that all of the victims will be fine and will survive these injuries," Queens District Attorney Richard Brown said. "We are hoping these young babies, small and so very fragile, are also strong enough to overcome this horrible act of senseless violence."
The suspect was found unconscious in the basement with self-inflicted slash wounds to her wrist. Police said she worked at the center.
She is in police custody at New York-Presbyterian/Queens, where she is also being treated for critical injuries. A motive hasn't been determined.
Police recovered a butcher knife and a meat cleaver at the scene.
WATCH Friday morning's update by police
Nine babies, five girls and four boys, were in the house during the stabbings, and all of them were accompanied by parents. Part of the building houses living quarters and the rest appears to be a nursery.
Police believe the stabbing location is a place where Chinese women, some of whom may have come to the US on visas, give birth to establish their child's residency. The women then leave the country and attempt to return at a later date.
Some community members referred to the location as a "maternity hotel" or a communal setting for immigrant parents who could not care for their newborns in the traditional way.
The local assemblyman said the female suspect was "in distress, most likely with some mental health illness, and had no business being around infants."
The New York City Department of Health issued the following statement:
"After the horrific incident at Mei Xin Care in Flushing, the health department is investigating the facility. Although it is still early in the investigation, the department can confirm that there was no home day care license for the location. NYPD is the lead on this investigation."