The women, 23 and 26, were arrested at 12:45 am near the shop on Bergsgatan in the city.
“They were outside the shop, and set fire to a phone book. They also tried to set fire to an antenna cable that led into the video store,” said police spokesman Lars-Håkan Lindholm to The Local.
As well as housing the porn shop, the block housed a number of apartments.
Police were called to the scene by someone who saw what the young women were doing.
It is not yet clear whether the women’s action was a political statement or whether they had another motive.
“They are going to be questioned. There’s nothing yet to indicate a motive. They had been drinking vodka however, and they were pretty drunk,” said Lindholm.
The women are suspected of attempted arson, but police say their attempt was a long way from being successful.
“It was pretty clumsily done,” said Lindholm.