A major rescue operation was launched at around 4.45pm, with five people pulled from the water and taken to Aberdeen Royal Infirmary.
The mother, 37, and her son died at the hospital, police said. Officers are currently making contact with the next of kin of the deceased.
A 28-year-old man, a 25-year-old woman and 13-year-old boy remain in hospital for treatment.
Chief Inspector Stewart Mackie said: “This is a very tragic incident which has resulted in a woman and young boy sadly losing their lives.
“It will undoubtedly bring shock and sadness to the entire city of Aberdeen and further afield.
“We urge anyone who witnessed the incident or perhaps have information that could assist, to make contact with police via 101.”