The animal was first reported to police earlier on Saturday evening as it roamed around the centre of the city.
According to eyewitnesses, it then climbed up a set of stairs to the balcony of a large apartment block near the bank of the Stångån river before leaping over the balcony's barrier, unaware of the large drop on the other side.
It was so badly injured on hitting the pavement that it was unable to get up and died before it could be put down by specialist hunters.
“It was walking around Drottninggatan and Repslagargatan, among other streets,” Björn Öberg, a spokesman for the local police, told Sweden's state broadcaster SVT.
“When the police arrived on the scene at 9.40pm, the elk was lying wounded on the pavement but was still alive. But by the time the municipal hunter arrived, it had died.”