Authorities say the stabbings happened just before 4 a.m. Friday at a home in Queens.
One of the babies is three days old and suffered a stab wound to the stomach, another is 20 days old and suffered lacerations to the ear, chin and lip.
CBS New York reports that the daycare was in a home and it was not yet clear if it was being run as a licensed care center.
Among the three children injured were two girls and one boy - all infants, authorities said. Police say the 52-year-old woman had slashed her left wrist and is in custody at a hospital.
Additionally, two adults were stabbed, neither of their injuries is said to be life-threatening. One of the girls was taken to the hospital in serious condition. Her relationship with the children wasn't immediately clear.
Police say they believe those wounds were self-inflicted. The man who was injured had a child at the day care while the woman was a daycare employee, according to NBC New York.
Officials have not determined a motive, according to WNBC.