Police said the youth was arrested on Sunday at around 4.30pm and had confessed to the murder. He had been to the crime scene - an apartment block in Davidgasse - to visit his brother, and numerous witnesses had reported seeing him on Friday when the murder took place, police spokesman Thomas Keiblinger said.
The police report said that the pensioner, who lived in the building, had got into an argument with the 19-year-old when she went into the stairwell to empty her rubbish and found him smoking there. She asked him to go outside to finish his cigarette, but he refused.
A while later he knocked on her door and allegedly punched her in the face - with such force that she fell over in her hallway. He then followed her into her apartment and continued violently attacking her.
The woman's body was discovered on Friday evening. The cause of death given was massive head injuries inflicted with a blunt object. She also had stab marks on her neck and upper body.
She lived alone in her apartment but was visited often by relatives and neighbours, who called the police when they could not reach her on Saturday.