It is not known what caused the children to become poorly and no adults have been affected.
One of the guests at the Pasha Bay hotel, Patrick Hagman, told TT that he, his wife and their four children had not fallen ill but said other children they met at the hotel were feverish and exhausted.
The Hagmans plan to remain at the hotel.
"Of course we are worried but I feel that since we haven't fallen ill we will be OK," Patrick Hagman said.
It is unclear whether the affected families will receive any compensation.
According to Mathias Bergendahl, a spokesman for Swedish charter travel agency Fritidsresor, the agency and the hotel must first investigate what happened.