Authorities say Abigail Daci was discovered in respiratory distress in the Klondike Avenue home just before 6:30 a.m.
She was rushed to Staten Island University Hospital North and pronounced dead.
The Medical Examiner's Office will determine the cause of death. There were no signs of trauma on her body.
The family had no history with the city's Administration for Children's Services.
Sources say Daci was part of a set of triplets.