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The bear, an adult male weighing around 250kg, was presumed to have swum to shore from drifting ice. The last time a polar bear came ashore in Iceland was in 1988.
Police Superintendent Stefan Vagn Stefansson said they shot the bear in order to protect the public after a plan to anaesthetize the animal was abandoned.
"There was a lot of fog in the area and the bear was moving into the fog.
"We couldn't risk losing him and there was no time to wait for anaesthetics, so we had to shoot him. It was for the safety of the public."
In response to a public outcry at the shooting, the environmental ministry said it would review the incident to see if it could avoid shooting the next bear that lands in the country.
The world's largest land-based predator lives in the Arctic, depending largely on sea ice to hunt seals.
When bears have come to Iceland they have usually travelled most of the way on icebergs from the east coast of Greenland. The animals are excellent swimmers.
Last month, polar bears were listed as threatened under the US Endangered Species Act because their sea ice habitat is melting away.
The US Geological Survey says two-thirds of the world's polar bears - 16,000 - could be gone by 2050 if predictions about melting Arctic sea ice hold true.
- REUTERS
