The woman, who was flown home from Sierra Leone on Sunday, was admitted to Skåne University Hospital and tested for the virus on Monday.
But after initially being told she did not have Ebola, she is now back under medical supervision at another hospital in the region as doctors carry out further tests.
"She has exhibited symptoms that could indicate Ebola, but it is not certain that it is [Ebola]," Sara Frostberg Lowery at Region Skåne's press office told the TT news agency.
"She has been transferred to the University Hospital in Malmö and after an assessment she will be transported to another medical centre in Linköping," she added.
There have been a handful of Ebola scares in Sweden since the virus started to spread rapidly in west Africa last year, but no Swedes have contracted it.
The World Health Organization reports that the disease has claimed 7,500 lives so far - the vast majority in western Africa.
Sweden has donated 550 million kronor ($69 million) in the fight a against Ebola.