The two women, aged 54 and 37, were found dead around 3am on Saturday morning after an ambulance had been called to an apartment in the town's Degeränget neighbourhood.
Ambulance workers in turn called police.
"In the apartment they found two dead women," said investigator Per-Olov Andersson of the Norrbotten County police to news agency TT.
According to police, the women hadn't been dead very long when officers arrived.
"The apartment is home to one of the women and we believe they were found right around the time they died," he told the Expressen newspaper.
A 31-year-old woman who is an acquaintance of the two deceased women is being held by police on suspicion of having caused their deaths.
The ambulance was called by someone who knew the women, but police refused to confirm if the 31-year-old woman being held in the case is the same person who placed the call to emergency services.
Police have interrogated the woman, but won't divulge how she responded to the accusations.
According to the police, all three women are known to have spent time among a group of known drug addicts in the city.
"It may be that someone took too much, and that another person is therefore suspected of having made that happen," Andersson told Expressen.
However, police refused to comment further on the details of the cause of death pending the outcome of an autopsy.