Three of the injured group were airlifted from the slope at the Lecht Ski Centre near Tomintoul, Aberdeenshire, while the others were taken by ambulance.
They are understood to have back and leg injuries.
A spokeswoman for the Lecht centre said 36 other people who were stranded on the chairlift were rescued after the accident at around 3.25pm today.
The spokeswomansaid: "All the casualties are in a stable condition, three were taken to hospital by helicopter and three by ambulance.
"Staff evacuated 36 people that were stuck on the other chairlifts and everyone was off the slope within an hour and 40 minutes.
"We don't know the reason for the accident, however the Health and Safety Executive and the Lecht will be investigating the cause."
Grampian Police, fire service and mountain rescue teams assisted with the rescue.
A force spokesman said: "Six people - five children and one adult - have been taken to hospital with what are believed to be non life-threatening injuries.
"Grampian Police and Braemar Mountain Rescue Teams were mobilised to assist with the rescue of those stranded.
"Units from Grampian Fire and Rescue Service, the Scottish Ambulance Service and local doctors were also called to the scene to assist.
"Inquiries are ongoing to establish the cause of the incident."
The Lecht, like Scotland’s other ski centres, have been enjoying good business since late last week with the half-term school holidays.
In a previous accident, in July 2006, a gondola plunged 25ft after smashing into another lift at Aonach Mor near Fort William.
A family of three, including a three-year-old girl who broke her leg, were among those injured in the crash.
Around 110 people who were stranded in the cable cars and at the gondola stations were rescued from the mountain, many by helicopter.
The cable car system was closed immediately after the accident and re-opened around two weeks later.