The Airbus 330 aircraft landed safely at Madrid airport on Tuesday night after suffering a 15-second episode of clear air turbulence which caused the plane to drop 100 metres (328 feet), Evelop said in a statement.
Fourteen people suffered light bruises and were taken to local hospitals for treatment, it added. They were all discharged on the same day.
Three flight attendants were among the injured, an Evelop spokesman said.
One passenger, who gave only her first name, Mar, told news radio Cadena Ser that the plane “plunged like when you are at a fairground attraction.”
“We saw many passengers fly literally over the seats, some hit the ceiling, others the seats beside them,” she added.
The airline said the seat belt warning activated before the plane flew into the turbulence zone.
Clear air turbulence is turbulence that occurs in otherwise calm, clear blue skies, without any visual indication such as clouds.
Evelop, which is based in Spain's Balearic Islands, operates short and long haul flights out of Spain and Portugal on behalf of tour operators.