Fire chief Per-Erik Thyberg told TV4 Skaraborg that the alert was raised just before 4am. Two sections of Fjäril school in Södra Ryd, which was being used as a kindergarten, were ablaze.
The school consisted of three parts, each of up to 200 square metres. The two sections which caught fire were completely destroyed.
Around 25 firemen from three stations were called in to fight the fire, which also threatened another nearby school.
This latest fire was started despite the fact that Skövde council, after four fires in three weeks, decided that all nursery schools should be monitored at night. The supervision was to be carried out by the police and a security firm.
Late on Monday evening another two nursery schools were set on fire, but the damage was limited thanks to a call from a member of the public and a quick response from the fire brigade.
A police spokesman told TV4 Skaraborg that one person was arrested on Monday on suspicion of arson but then released at around 8pm. Whether that person is still under suspicion was unclear.
Many of the children who attend the preschools have not yet been found an alternative daycare location.
“Around 55 children are without a childcare place,” said Britt-Marie Bladh, a schools administrator in Skövde on Tuesday.