A helicopter took off on a search and rescue operation after the crew of a fishing boat told the border guard earlier this week that they had spotted the bear drifting in the Baltic Sea off the coast of Ruhna island.
"Our attempts to find the bear did not succeed and we had to return to shore empty-handed," border guard spokeswoman Helena Loorents said.
"Visibility became too bad. We had to terminate the search," Ms Loorents said.
"We have informed fishing vessels in the region about the bear so that they could notify us immediately if they spotted the bear again," she said.
Nature conservation experts said the bear may have been a young animal who had been 'sent away' by its mother. Spring is the season when young bears usually set off in search of their own territory.
"It may have climbed onto the ice to get something to eat, and ended up on the ice floe," Enn Vilbaste, a nature conservation official, told local press. "The bear's chances of getting back to land are slim," he said.
Experts said this was the first time they had heard of a bear finding itself adrift and alone on an ice floe.