The infected person is a man born in 1984 who recently returned from New York, health authorities said.
"He has been sick for three days but is holding up well," said a statement from the Swedish Institute for Infectious Disease Control (Smittskyddsinstitutet (SMI)).
According to the incident the man, who lives in Stockholm, is being cared for by health authorities and is feeling well under the circumstances and is no longer contagious.
"It is someone who has been travelling in New York and come home with flu-like symptoms. After tests we found that he had the new influenza," confirmed Mia Brytting at SMI.
Sweden confirmed its first case of A(H1N1) influenza, as the swine flu virus is officially known, on Wednesday after a woman in her 50s, who had also just returned from the United States, tested positive for the disease.
SMI is unable to speculate as to how many cases of swine flu that Sweden can expect to confirm.
"We encourage all returning travellers from the USA and Mexico to seek care if they experience flu-like symptoms," Mia Brytting said.
On Sunday two cases were also confirmed in Norway bringing the total number of infected in Scandinavia to five.