The Danish Health and Medicines Authority said on Thursday that the patient's blood sample would be analysed at the State Serum Institute (SSI) and the results were expected to be available later on Thursday.
The patient, who is a member of the aid group Doctors Without Borders, returned from West Africa recently with fever symptoms, according to the Danish news agency Ritzau.
If confirmed, it would be the first Ebola case reported in Denmark.
Since March this year, the Ebola outbreak in West Africa has killed nearly 4,500 people and there have been confirmed or suspected cases of Ebola in the US, Spain, Germany and Norway after people have returned from affected countries in Africa.
The Ebola virus can cause fever, bleeding, vomiting and diarrhea and is spread through contact with bodily fluids.