The emergencies ministry said that 48 people were involved in the rescue operation, two helicopters and 11 ships weere used to fetch the people of the moving ice sheet.
Fishing through bore-holes on ice-bound waters is a popular winter pastime in Russia.
Taymuraz Kasayev, of the emergencies ministry, said the area's residents had been told to stay away from the ice.
"We warned people through the media that going out on to the ice on this stretch of the coastline is extremely dangerous and is not allowed," he told the NTV television channel.
One of the rescued anglers, Vladimir Vasilenko, said he had ventured on to the ice floe knowing that the windy conditions might pose a risk.
"The wind was blowing from the shore, and it was clear that something might happen, but people were still going out, so we did too," he said.
"It was the excitement, of course. We also heard on the radio that it would be the last chance for fishing on the ice. And so we rushed out to go fishing."