The five-storey block of flats in Los Cristianos on the Spanish island collapsed close to a Swedish school and a Swedish church on Thursday morning.
Witnesses reported hearing a blast and smelling gas before the building was reduced to rubble.
“It sounded like a bomb had exploded,” one neighbour was quoted as saying by the Swedish tabloid Aftonbladet.
By mid-afternoon, emergency services said that a 57-year-old woman had been seriously injured and two others were hurt, however their nationalities had not been revealed.
Nine other people believed to be staying in the block were still unaccounted for by 4pm.
Sweden's Foreign Ministry said it was looking into the possibility that Swedes had been caught up in the collapse.
“We are investigating the matter with the help of the Swedish consulate in Gran Canaria,” press spokesperson Karin Nylund told the TT news service.
Meanwhile Sarah Pallin, a Swedish journalist who lives just a few blocks from the collapsed building told Swedish tabloid Aftonbladet that a huge search operation had been going on.
“There were several ambulances and rescue vehicles (…) now they are looking for people in the rubble with search dogs,” she said.
“The rescue operation is impressive, it's completely cordoned off in all directions.”
Spain has been a popular destination with Swedes for decades and was the favourite country overall for Swedish people booking summer breaks in 2015 according to a poll by Novus.
As well as the sunshine, lower meal and alcohol costs are thought to play a key factor in Swedes choosing to travel to Tenerife and other Spanish islands.
“In southern Europe food, drink and activities are still much cheaper than in Sweden,” Aud Bengtsson, a spokesperson for Scandinavian travel firm Sembo, recently told The Local.