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The mother, a Polish national, dived overboard in a desperate attempt to save her seven-year-old after he fell off the vessel into the icy Baltic Sea on Thursday.
He is thought to have fallen from a height of about 20 metres (65 feet), according to Swedish Maritime Administration spokesman, Jonas Franzen.
NATO ships are said to have been scrambled in the rescue operation, which saw the pair winched to a helicopter.
They were transported separately to a hospital in Sweden, but could not be saved, authorities said.
A preliminary murder investigation has been launched in the wake of the tragedy, Swedish prosecutors announced on Friday.
However, a suspect has yet to be identified.
Prosecutor Stina Brindmark said: "The investigation aims to clarify what happened."
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The deaths of the mother and son, who have not yet been identified, were earlier confirmed by Polish police.
A police spokesman, Mariusz Ciarka, said: "Unfortunately, in the morning we received information from the Swedish side that we have to pass on this terrible news to the family, because both the boy and the woman are dead."
The Stena Spirit ferry departed from Karlskrona in southern Sweden, around 500km (310 miles) from the capital Stockholm.
It was midway through its journey to Gdynia on the coast of Poland, about 450km (279 miles) north of Warsaw, when the incident happened, rescue officials said.
Authorities also investigating potential ferry malfunction
"At the moment we have no information whether this was due to a malfunction of the ferry," Stena Line spokesperson Agnieszka Zembrzycka told Polish news channel, TVN 24.
"We are cooperating with the police and other authorities that are appointed to explain the causes and circumstances of this event."
Swedish police have issued an appeal to Polish passengers via Poland's state-run news agency PAP asking for information that could explain how the deaths occurred.