The patient is a woman in her 20s who landed in Sweden on January 24th after visiting the Wuhan area in China. At that point she had no symptoms, said the agency.
But a few days later she developed a cough and contacted the health services in Jönköping.
She is currently being kept in isolation at the clinic for infectious diseases and is not seriously ill.
“It is important to remember that individual cases is not the same thing as the infection spreading in Sweden. We currently consider this risk to be very low based on experiences from other countries,” Karin Tegmark Wisell, head of the Public Health Agency's department for microbiology, said in a statement.
The woman had not been in contact with other people since returning to Sweden so there is no risk of her having spread the virus, Malin Bengner, an infectious diseases doctor in Jönköping, told a press conference on Friday afternoon.
Swedish health officials said the woman had followed their guidelines when she developed symptoms, by calling the health services to explain the situation rather than showing up at hospital in person.
“She has acted in an exemplary way,” Tegmark Wisell told reporters via a telephone link.
Around 20 people have so far been tested for the coronavirus (2019-nCoV) in Sweden, but all tests apart from the one patient in Jönköping have come back negative.
The coronavirus broke out in the Chinese city of Wuhan – which is an international transport hub but has no direct flights to Sweden – at a fish market in late December.
The World Health Organization on Thursday declared the outbreak a global emergency, as the death toll exceeded 200 and China's health commission reported more than 9,600 confirmed cases of infection.
At least 80 infections have been reported outside of mainland China, Hong Kong and Macau.
The symptoms of the coronavirus are not dissimilar from a common cold.
They include a cough, headache, fatigue, fever, aching and difficulty breathing, and the virus is primarily spread through airborne contact or contact with contaminated objects.
If you think you may have the coronavirus, do not do not go to hospital or your doctor's surgery. Swedish health authorities are worried about potentially infected people turning up at hospitals and passing on the virus. Instead, call Sweden's national health advice hotline 1177.