It is understood that two brothers, aged six and 13, were paddling in the water when they were swept away. Their mother and others tried to save them.
The emergency services arrived at 16:45 on Saturday.
Five people were taken to Aberdeen Royal Infirmary, where a 37-year-old woman and a six-year-old boy were pronounced dead.
The 13-year-old boy, a 25 year-old woman and a man, 28, remain in hospital receiving treatment. Their condition is not known.
Police Scotland has launched an investigation and officers are searching the scene.
Witness Emma Anderson was in the area at the time and told the BBC she heard sirens and police "frantically" telling people to evacuate the area.
"The whole boulevard was covered in ambulances and police. We overheard there was a body in the water and we saw what seemed to be the body of a small child floating lifelessly in the sea," she said.
"This is something that will forever be in my mind. Not something I ever expected to see on a fun day out with my kids. Heartbreaking for all involved."
Rachel McBain, 25, who rang 999, told the Sunday Mail newspaper she saw two children go into the waves.
"I turned away for a few minutes and when I looked back I saw the two bodies floating in the water," she said.
"I was panicking but phoned the police. The next minute it was absolute chaos and there were sirens within seconds."
Ch Insp Stewart Mackie described it as a "very tragic incident".
He added: "It will undoubtedly bring shock and sadness to the entire city of Aberdeen and further afield.
"Given the recent weather conditions we'd urge members of the public to take care, especially when near coastal or beach areas."
He also asked anyone who witnessed the incident to make contact with police by calling 101.
First Minister Nicola Sturgeon said the news was "heartbreaking".
She tweeted: "Tragic, heartbreaking news. My thoughts are with all those involved."
Police are currently making contact with the next of kin of the deceased. Fire crews, coastguards and the ambulance service were involved in the rescue effort.
The Maritime and Coastguard Agency said some people had been pulled out of the water by police and others had been rescued by the inshore lifeboat.
A mother and son have died after five people got into difficulty in the sea off Aberdeen beach.