"Several buildings were burnt, including one which witnesses say has been destroyed completely," police said in a statement.
"For the moment the cause of the fire is not certain but as there are reasons to suspect it may have been started deliberately, a preliminary arson inquiry has been opened."
The planned shelter, on the outskirts of the town of Floda in southwest Sweden, had yet to welcome its first residents. There were no injuries and there have been no arrests.
Total arrivals of asylum-seekers to the Scandinavian country are expected to reach up to 1,90,000 in 2015, the most per capita of any European nation as the continent struggles with its worst migration crisis since World War II.
On Thursday the Swedish government warned that its capacity to host the refugees has reached saturation point and it cannot guarantee shelter for any new arrivals.
"We are in a tense situation and we are dependent on the opening of new lodgings. It is incredibly hard when they are destroyed by a fire," migration agency spokeswoman Johanna Uhr told the Goteborgs-Posten newspaper.