The patient on Tuesday showed symptoms of fever, headache and muscle pain, Xinhua news agency reported citing an official of Aarhus University Hospital, where the patient was hospitalised, as saying on Wednesday.
The Dane was in good condition and was in outpatient care, he said.
The Zika virus originates from and is transmitted by mosquitoes and can cause microcephaly in fetuses.
Symptoms of Zika include low-grade fever, joint pain, rash, conjunctivitis, headache, muscle pain and eye pain.
The Danish health authority denied on Tuesday the risk of a Zika virus outbreak in the country but advised pregnant women to postpone non-essential journeys to Latin America, where an outbreak of the virus is ongoing.
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