"This Sunday morning, due to strong winds... there was an incident caused by a tree falling close to the Tomahawk ride," the theme park, a favourite with tourists to Spain's Costa Dorada, said in a statement.
"Some of the branches hit visitors who were on the ride," the statement continued.
Catalan emergency services said they had attended to 14 people. Two in a critical condition were taken to two separate hospitals. Three people in a less serious condition were also taken to hospital.
The Tomahawk ride is a "children's roller coaster with frenetic climbs and descents," according to PortAventura's website.