Four people, including two children, were taken to hospital by ambulance while the rest of the injured were treated at the scene in the Mediterranean port of Alicante, an emergency services spokesman said.
The injuries were mostly scratches and bruises caused by falls or people being knocked into each other, he added.
"It all happened in a few seconds. Five inflatable castles went flying and they moved about 100 metres with children inside them," Alicante town councillor Manuel Marin, who was at the scene at the time, told reporters.
"We must determine responsibility and prevent this from happening again," he added.
Police have seized the inflatable castles and cordoned off the area as part of an investigation into the accident.