The injured infants ranged from three days to one-month old, police said. One woman suffered multiple stab wounds to the torso, while a man received a stab wound to the leg.
The motive was not immediately clear.
A 52-year-old female "babysitter/worker" at the in-home center was arrested, police said. The stabbing took place in the borough of Queens shortly before 4:00am (0800 GMT).
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The suspect had a slash wound to her left wrist, police said. Two knives were recovered at the scene and all the injured were taken to hospital in a critical but stable condition, police told reporters.
Police said earlier that the suspect attacked two baby girls and a baby boy, leaving one of the girls in a serious condition. None of the victims' lives was in danger, police said.
The wounded female victim worked at the daycare, while the other was the father of one of the babies.
Nine babies and some of their parents had been at the home at the time of the attack, police said.
Officers found the suspect in the basement of the center with a self-inflicted cut to her wrist.
A police spokesperson earlier said that the childcare center appeared to be an "illegal" facility for members of the city's Asian community, but officers later clarified that its status was unclear.
The in-home center appears to have functioned for several years, as police responded to a noise complaint from neighbors in 2011.
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