A visitor to the YouTube site alerted police to the content of the video on Tuesday.
“We are taking the threats very seriously,” police spokesman Stefan Gustafsson told the TT news agency.
In the video, which is of very poor technical quality, a man wearing a hood, dark glasses and a scarf addresses the camera and speaks of his plans for a bloodbath at the Nordstan shopping centre.
“The nasty old men will be executed. October 30th, 12.30, Nordstan. I swear, they’re going to die,” he says.
“His voice is distorted and it is difficult in places to hear what he is saying, but the main thrust is that there will be people killed or murdered at Nordstan at lunch time on Thursday,” said Gustafsson.
Police said they were now focusing on identifying the person or people behind the video and securing the area in and around the shopping centre.