The bear, an adult male weighing around 250kg, was presumed to have swum some 300km from Greenland or from a distant chunk of Arctic ice to Skagafjordur in northern Iceland.
It was planned to sedate the animal and move it back to Greenland but the police decided it was safest to kill the bear immediately.
"There was fog up in the hills and we took the decision to kill the bear before it could disappear into the fog”, said police spokesman Petur Bjornsson.
Environment Minister Thorunn Sveinbjarnardottir gave the green light for police to shoot the bear because the correct tranquiliser was not available in Iceland and would not be flown in for a day, Icelandic news channel Visir.is reported.
However, a veterinarian said he had the drugs available in his car. He also criticised police for not closing a mountain road where people congregated after hearing news of the bear.
Polar bears were recently listed as a threated species by the US because its Arctic sea ice habitat is melting due to climate change.Why they must be saved: Knut, the world's most famous polar bear
US government scientists have predicted that two-thirds of the polar bear population of 25,000 could disappear by 2050.
The shooting came as the Japan Whaling Association revealed it could justify an increase its minke whale kill to "tens of thousands" based on data it says shows an abundance of the giant mammals in the Antarctic.
Japanese whaling spokesman Glenn Inwood told The Australian newspaper the research would be presented at the next International Whaling Commision meeting.
"It is certainly hopeful that when that figure is run through the quota system of the IWC that it will be looking at the sustainable harvest possibly of tens of thousands of minke whales each year," he said.
"This new abundance estimate for Antarctic minkes will be one of the greatest threats to Australia's position on whaling. It will be very hard to deny Japan a quota."
Also at the conference will be teenage anti-whaling crusader Skye Bortoli, who will be taking The Daily Telegraph's fight right to the top.
The 16-year-old is getting ready to travel to Chile for the annual conference, where she will lobby for a worldwide ban on the slaughter of whales.