It has been viewed more than 19 million times on social media.
However, experts have suggested the whale could be none other than Hvaldimir, a male beluga who is thought to have been trained by the Russian navy, The Independent reported.
Hvaldimir was first spotted near Norway in April 2019.
A harness was attached to his body and a label that said "Equipment of Saint Petersburg".
He is known to approach boats to ask for food and play fetch, and is thought to have been hand-fed by humans and not able to successfully hunt for himself.
Ferris Jabr, a science writer, said he believed the whale on the video was likely to be Hvaldimir, as did Quad Finn, a researcher of aquatic mammals.
Finn said: "Hvaldimir was taken from the ocean and trained by humans to do tricks like fetching objects in exchange for food.
"That he's malnourished and still dependent on humans for food are likely reasons for what appears to be 'playful' behaviour."
Both Russia and the United States are known to have military training programmes for aquatic mammals.
However, in April a Russian military spokesperson denied that Hvaldimir was connected to any training programmes.
In the video, the beluga whale can be seen swimming up close to the boat and allowing a person onboard to take a rugby ball out of his mouth.
When the ball is thrown back into the sea the whale swims after it, before bringing it back to the boat for it to be thrown again.