“We don’t know anything yet. We just know that he’s alive… It’s some kind of miracle!” she told the Russian agency.
She also said their daughter was supposed to go on the ill-fated trip, but she had decided she wanted to return home.
A helicopter search had found no trace of the trio after their disappearance was reported, according to RIA.
The boat was discovered on Monday as it floated past a fishing boat in the Sea of Okhotsk, off the coast of Kamchatka Peninsula, which lies in the far east of Russia, the Russian news agency reports.
A bearded man in a life jacket is seen shouting at the fishermen: “I have no strength left,” as he is taken to safety, in a video posted by the prosecutor’s office.
He was named by RIA as 46-year-old Mikhail Pichugin. The bodies of his brother Sergei, 49, and nephew Ilya, were still on the boat.
As to how he was able to survive for so long in the Sea of Okhotsk – the coldest in East Asia – a representative from the far eastern branch of the Russian seafarers’ union suggested a supply of fish may have played a part.
Nikolai Sukhanov, told RIA Novosti in such a situation you can survive by catching fish while eking out whatever provisions are left on the boat.
Mr Pichugin is now recovering in hospital, where he is described as being in a “more or less stable” condition by doctors.
Prosecutors have said they are launching a criminal investigation, with the small boat being inspected and investigators trying to establish the circumstances into the incident.
It is not the first time that castaways have been found after many days adrift – an expert told the RIA Novosti four Soviet soldiers had survived 49 days adrift on a small boat in the Pacific Ocean in 1960, before being picked up by a US aircraft carrier.