Doctors said the child's condition was improving.
A suicide pact may have preceded the shootings, investigators said.
The baby was found after neighbors informed authorities of a strong odor emanating from the family's residence in the city of Goya last week, the Latin American Herald Tribune reported Monday.
Police found the bodies of Francisco Lotero, 56, and Miriam Coletti, 22, and their 2-year-old son. Lotero and his wife had gunshot wounds to the chest and their son was shot in the back, investigators said.
Officers found the little girl in another room.
Doctors said the infant's condition had continually improved.
The Herald Tribune said a note found in the family's home led authorities to suspect the deaths were the result of a apparent suicide pact brought on by concerns about global warming.
Celebrity Families of 2014 [PHOTOS]