The women, aged 68 and 38, died when the "Dreamspace" inflatable exhibition broke its moorings at Riverside Park, Durham, northeast England, and was blown into the air, said Durham Police spokeswoman Joanna Banford.
A 3-year-old girl is in a serious condition following the accident, and 11 other people, both children and adults, were also injured, she said.
Police said up to 30 people were on the structure when it flew into the air. It came down after striking a metal pole.
John Robson of County Durham and Darlington Fire and Rescue Service said there were scenes of chaos in the park where the inflatable came down.
"There were parents looking for children, children looking for parents," he said. "We had to extricate a number of people from the structure. A number of people had fallen on top of each other."
"Dreamspace", a temporary construction made of thin translucent PVC sheets, was an inflatable 2,500 square meter (8,200 square foot) structure, designed by artist Maurice Agis, which allowed adults and children to climb aboard and crawl through its networks of multicolored tunnels.
An investigation into the cause of the accident has begun.