Around 120 people at La Rambleta, the upper of the two stations more than 11,600 feet above sea level, were brought down later after a three-hour wait.
It is understood they were rescued using the gondolas, which had to be operated manually at a slower speed than normal.
The alarm was sounded around 10.20am this morning when the cable car service broke down for reasons that are still being investigated but have been blamed on the failure of a motor used to operate it.
Emergency services were mobilised including local firefighters who helped those affected reach safety.
No-one needed medical attention although local reports said a Spanish woman trapped inside one of the gondolas suffered a panic attack.
It was not immediately clear if any Brits or Irish were involved.
A spokesman for Volcano Teide Experience tweeted: “Around 10.20am today the security protocol was activated after the cable car service stopped functioning.
“At that moment in time 34 people were in a gondola who now at the base station being evacuated.”
Some 120 people are still at an upper station who are going to be evacuated immediately.
A spokesman for the Volcano Teide Experience
“Some 120 people are still at an upper station who are going to be evacuated immediately.
“We will be closed for the rest of the day so we can make the relevant checks and will probably open tomorrow.”
After initially saying they hoped to open tomorrow, the cable car firm later said the service would be closed all weekend.
In a second tweet after the rescue was completed, it said: “There were 34 customers in the cable cars who were brought down in the same cars.
“The visitors who were at La Rambleta, around 110, were also brought down to the base station using the cable car service.”
A spokesman for a local emergency services coordination centre confirmed: “Tenerife firefighters have participated in the rescue of the people who were affected by the cable car breakdown, accompanying them as they were brought down to the base station.”
In March last year nearly 250 tourists were affected after the service broke down, leaving dozens of passengers trapped in two gondolas and forcing more than 100 to spend the night at high altitude.
Around 70 tourist ‘abseiled’ 250ft to safety in a dramatic rescue.
Helicopters, firemen, police and park rangers were called in to help with a pulley system to get the trapped tourists back on the ground.
The were lowered to safety one by one during a four-hour rescue operation which involved placing them in a harness before they were dropped through the cable car hatch.
Nearly 200 people at the top of the cable car who had already visited Mount Teide were waiting to come down at the time and most ended up walking to safety despite the rock terrain.
Other people including elderly holidaymakers and families with children spent the night in a refuge on the mountain.
The base station of Teide Cable Car is at the foot of the Tenerife volcano, at a height of around 7,730 feet.
The cable car service saves visitors a long and arduous walk to the summit.
Mount Teide’s 12,198ft summit is the highest point in Spain.
The volcano and its surroundings, a popular attraction with foreign holidaymakers, comprise Teide National Park which was named a World Heritage Site by UNESCO in June 2007.
Teide is the most visited natural wonder of Spain and the most visited national park in Spain and Europe.
It attracted more than four million visitors in 2016.