The 22-foot Bayliner speedboat overturned at about 10:25pm (local time) on Saturday near Liberty Island, home to the Statue of Liberty, the US Coast Guard said.
Twelve people were rescued from the water before police arrived. According to the US Coast Guard, they were in stable condition.
Police divers later located the 27-year-old woman and a five-month-old girl in the water.
Both were taken to a hospital where they were pronounced dead.
"We are deeply saddened by the tragic loss of life last night, and our thoughts are with the victims' family and loved ones during this incredibly difficult time," Captain Doreen McCarthy, from the US Coast Guard, said.
"We are extremely grateful for the heroic, swift actions of our partner agencies and the good Samaritan vessel who assisted in rescuing survivors from the water."
The victims' identities have not been released pending notification of family, police said on Sunday.
A 46-year-old New York man has been charged with 13 counts of reckless endangerment.
An illegal charter is any passenger-for-hire vessel operation that lacks US Coast Guard credentials, safety equipment and inspection certificates.
