The band debuted the clip on their official YouTube page, marking the second in their 'Valtari Mystery Film Experiment'.
The project involves 12 filmmakers who have been given the same budget and asked to create what comes into their head when they listen to a song from their new album Valtari.
They said: "We never meant our music to come with a pre-programmed emotional response. We don't want to tell anyone how to feel and what to take from it.
"With the films, we have literally no idea what the directors are going to come back with. None of them know what the others are doing, so hopefully it could be interesting."
Sigur Rós's latest album entered the US album chart at number seven, and reached number eight in the UK.
Watch the short for 'Varúð', directed by Inga Birgisdóttir, below: