Mayerly Diaz Rojas and her husband Fabio Grandas died in the HK 2335-G plane a few hours after leaving Santa Marta for Guaymaral.
But their baby, Martin, miraculously survived and was found by rescuers.
The infant is said to be in stable condition and, according to local media, is being treated at the Fundacion Santa Fe University Hospital in Bogota.
The plane descended in Ubate, Colombia on Tuesday afternoon.
Martin’s nanny, Nuris Maza, is also deceased – the cause of the horror crash is not yet known.
Aviation authorities say they are investigating what went wrong on board.
In the statement, they said: “According to initial information, the aircraft had all its technical documentation up to date. “
Mr. Grandas was piloting the light aircraft, it is reported.
The Colombian Civil Aviation Authority expressed its “solidarity with the families of the victims” in a statement.
They added: “A baby, who was also traveling on the plane, is currently being cared for in an assistance center.”
Rescuers found the mother was still rocking the baby after using her body to protect it during the crash, local media confirmed.