The flight was meant to be the highlight activity at the end of the week-long camp, where youngsters got the chance to ride in a plane after days spent learning about aviation.
"My world has collapsed", said Yves Burkhardt, the general secretary of the Swiss aviation group Aero-Club that runs the camp.
He called the crash of the single-engine plane in the canton of Graubunden "extremely tragic". Police said a probe into the accident in the mountainous region has been opened.
The club has been operating youth summer activities in Switzerland for 35 years, Burkhardt said.
The aircraft was identified as a Piper PA28, a light plane sometimes used for training.
The downed plane passed a full technical inspection last month, officials said.
The pilot was experienced and had already taken another group of campers up for a flight earlier in the day, area police spokesman Roman Ruegg said.
According to Ruegg, a group of tourists who had taken a gondola ride up to view the region's peaks watched the plane plummet at around 9:30 am (0730 GMT).
The crash occurred not far from the Diavolezza cable car stop high in the Alps, a popular tourist attraction in the Engadine region.
Swiss federal aviation authorities have ordered a ban on all flights within 4.5 kilometre (2.7 mile) radius of the area, ATS news reported.
The Engadine area has endured a particularly sombre week.
Four climbers have died in two separate incidents this week while trying to ascend the Piz Bernina, one Engadine's most famous peaks.
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