The woman was stabbed to death with a knife. The man found alongside her in the apartment was taken to hospital to be treated for serious injuries.
The police remain on the lookout for more suspects, and said they already have some leads.
“There were several witnesses, and some say three people in hoodies ran in the opposite direction of the two people who were arrested,” Kristoffer Bang of the Oslo police told the Verdens Gang (VG) newspaper.
The paper reported that the woman had lived in her apartment for one year, but had in the last week been scared to be there after it was burgled.
Her landlord, Dag Håland, told the Norwegian paper that the woman “seemed to be a typical, friendly, decent young Swedish girl”.
The Oslo police will hold a press conference at 5pm, and have refused to give out any more details until then.