According to newspaper Correio da Manhã the woman was found lifeless near a lift inside the building on Rua Amélia Rey Colaço.
The murder is believed to have happened during the early hours of last Friday morning.
A 19-year-old believed to be the perpetrator of the crime was detained by authorities and taken to Lisbon’s Santa Maria Hospital to be treated for injuries.
He was arrested after being reported by a passerby who spotted the teen on the street, covered in blood and wielding a knife.