Swedish authorities said on Thursday the child had fallen off the vessel and that the mother jumped overboard in an attempted rescue. The two were later winched to a helicopter and taken to a Swedish hospital but later died.
But the Swedish prosecution authority said in a statement on Friday it had initiated a preliminary investigation where the criminal charge is murder, while adding that no suspect had been identified.
"The investigation aims to try to clarify what happened," prosecutor Stina Brindmark said.
Polish police had earlier confirmed the deaths.
"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," said Polish police spokesman Mariusz Ciarka.
The Swedish ferry, Stena Spirit, was in the Baltic midway through its journey to Gdynia in Poland from Karlskrona in Sweden when the incident occurred, rescue officials said on Thursday.
"At the moment we have no information whether this was due to a malfunction of the ferry," Stena Line spokesperson Agnieszka Zembrzycka told 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 issued an appeal to Polish passengers via Poland's state-run news agency PAP asking for information that could explain how the accident occurred.
(Reporting by Terje Solsvik in Oslo, Alan Charlish in Warsaw and Anna Ringstrom in Stockholm; editing by Mark Heinrich and Alistair Bell)
