Rescuers rushed to the Butterfly Disco Club in Adeje at about 2:30 am (0230 GMT) after a roughly four square metres (43 square feet) of its floor gave way.
The injured included two French men aged 38 and 40, two British men aged 57 and 59, a 45-year-old Romanian man, and a 23-year-old Belgian woman, the regional government of Spain's Canary Islands said in a statement.
"After the floor collapsed, the people who were inside fell to the basement from the height of approximately one floor," it said.
Video posted by the local fire department on Twitter showed firefighters picking through rubble with their hands in the basement of the nightclub located in a shopping mall.
Firefighters remained at the scene until 6:00 am to search the basement in case anyone was trapped inside.
Authorities said the basement was not in use and so was empty at the time of the collapse.
The club is in Playa de las Americas, an area popular with tourists on the Spanish island.
Britain's foreign office said it was in contact with "a number of British nationals" who had been injured in the incident.
Videos posted on social media showed emergency services workers attending to people on the ground or on benches outside of the nightclub.
Checking other buildings
Emergency services took 21 people to hospital and treated another person at the scene who was released, the regional government said.
Another 18 people went to hospital by their own means to be treated, the mayor of Tenerife said.
The injuries included broken legs, ankle sprains and bruises. Two of the injuries were deemed serious.
The Butterfly, a popular gay nightclub in Tenerife, features drag shows and Go-Go dancers on Saturday nights, according to its Facebook page.
Video posted by Tenerife firefighters showed a gaping hole in front of the club's stage.
Police have launched an investigation into the incident.
The club had its licence in order and did not appear to be overcrowded when the floor caved in, Tenerife mayor Jose Miguel Rodriguez Fraga told a news conference.
All establishments in the shopping centre where the nightclub is located have been ordered shut as a precaution, he added.
"We are evaluating the three adjacent shopping centres to see if they were affected even though they are structurally independent," said Fraga.
Located off the west coast of Africa, the Canary Islands welcomed 13.3 million foreign tourists last year, making it Spain's second most visited region after Catalonia. Over half of the foreigners who visited the archipelago came from Britain and Germany.
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