Some 80 families are affected, according to local newspaper Sydsvenskan.
Several animals were discovered on Monday and rat inspectors have been called to the school to set traps for others.
"Our ambition is that all children should be able to come back on Wednesday," said Mariana Thelander who works at the school.
The situation is made more complicated by the fact that Sweden's Social Insurance Agency website is down.
In Sweden, the agency offers parents a benefit based on their salary, if they need to stay at home to look after their children because they are sick, rather than this cost being absorbed by employers. But mums and dads need to be able to log on to the site in order to register their absence from work.
It is unclear if parents will receive compensation for being forced to provide childcare because of the rat infestation.
"That I dare not say. We must investigate," Thelander told Sydsvenskan.
In March 2014, a family from Stockholm made global headlines after finding a giant rat in their kitchen.
The 40cm long creature had found its way into the apartment cellars by chewing through cement and wood.