Those arrested are between the ages of 20 and 50, and police believe the suspects may be connected to a number of other fires in the area, the Swedish news agency TT reported Wednesday.
Police officer Anders Goransson said the group might be connected to "four to five" other fires, adding "we think the numbers will grow."
He declined to mention any possible motives for the fires.
A blaze at the Naturbruksgymnasium high school in Ytterjarna, about 30 miles south of Stockholm, burned the school's giant barn to the ground in late March. Some 70 cattle died in the fire.