Around 20 pupils were travelling on the bus when it spun off a road as it turned a corner and landed on its side in a ditch.
Two children, both aged 12, were taken to hospital, but emergency services reported that neither had been seriously injured.
Police said they were investigating exactly what had caused the bus to come off the Karlsbyvägen road, but noted that there had been a number of accidents in the region, apparently caused by heavy snowfall and ice.
A tweet from a regional newspaper showing the bus on its side
Marie Staerk, a forecaster at Sweden's weather agency SMHI told the TT newswire that there had been upwards of 20cm of snow in some parts of Svealand and Götaland on Monday morning.
She warned that more snow could fall during the day, turning into sleet by the evening and forming ice overnight as temperatures drop below freezing again.
"Then it [the snow] may freeze and again it may become cumbersome in traffic," she said.
Sweden has one of the best road safety records in the world, but this morning's incident comes just weeks after a four-year-old was hurt in a high profile rush-hour smash in Stockholm.
Last month British indie pop band Viola Beach and their manager died after their car plummeted from a bridge in Södertälje. A preliminary report into the accident was released on Thursday.