The 18-year-old woman was taken to the Royal Sussex Hospital in Brighton after she fell about 15ft from the Rocker ride on Marine Parade in Worthing at about 9.30pm on Thursday.
She is understood to have suffered minor injuries.
John Mitchell, director for communities at Worthing Borough Council, said that the local authority is co-operating with the Health and Safety Executive which is investigating. He said: "Following an accident on a fairground ride at Worthing seafront our thoughts are with the woman injured in the accident and her family.
"We wish her a full and speedy recovery. We are grateful to the emergency services who attended the scene promptly.
"The fairground ride operators and Worthing Borough Council will fully co-operate with the Health and Safety Executive and relevant authorities into the investigation that will take place.
"In the meantime, the ride will remain closed until HSE clearance is received to re-open the ride."