The woman was found strangled to death the morning after celebrating her birthday in the apartment, the Aftonbladet newspaper reports.
Her body was discovered around 7am on Sunday morning.
“She lay dead in a bed recess and we suspect she was strangled,” a police source told the newspaper.
When police arrived at the apartment, they found a 33-year-old man who has since been detained on suspicion of murder.
According to police, the man is not a resident of Stockholm and doesn’t appear in the Stockholm police register.
Police refused to say, however, whether or not the man and woman knew each other.
The woman had until recently lived in Värmland in western Sweden prior to moving to Stockholm a few weeks ago and moving into a sublet apartment.