Sweden's agriculture agency (Jordbruksverket) issued the new guidelines on Tuesday after the World Health Organization warned European countries to be "vigilant".
The decision has the backing of Sweden's National Veterinary Institute.
"This is a precautionary measure," Katharina Gielen from the agriculture agency told news agency TT.
The WHO said that the H5N8 strain of bird flu discovered in the Netherlands was likely to spread to other animals, although it remained unclear if the virus would reach humans in Europe.
At a news conference in Geneva, WHO researcher Elizabeth Mumford told reporters that affected countries should "kill all sick birds" and closely monitor anyone who has been in contact with infected poultry, especially if they have a fever.
On Monday the European Commission banned the sale of poultry products from the areas of Germany, the UK and the Netherlands where bird flu has so far been discovered.
There are many different kinds of bird flu and most are harmless to people. But it is possible for the virus to spread to those who come into contact with sick animals.
Between 2003 and July 2014 there were 667 confirmed human cases of H5N1 infection in 15 countries, according to the WHO. It is believed that at least 393 people have died as a result of contracting the virus.