The deaths plunged the community in the town of Arnstein into mourning.
The five young men and a woman, all aged 18 or 19, were found on Sunday by the landowner whose son and daughter were among the victims.
Police say a wood-burning stove was in use at the hut, but other possible causes are still being investigated.
"The six adolescents... died from carbon monoxide poisoning," said a police statement.
"The cause of the leakage of the toxic gas remains under investigation."
The owner of the hut said he had gone there after his children failed to return from the party the night before.
A neighbour told German media that his daughter had been celebrating her 18th birthday.
The brick building is some distance outside the town and the area was covered in snow.
The tragedy has caused an outpouring of grief in the town, which is about 30km (18 miles) north of the city of Wuerzburg.
An area has been set aside in the local church for flowers, candles and other tributes to the teenagers. A gathering for friends and relatives was held there on Monday "for grief, remembrance and prayer".

Hooker Hughes, 20, featured for Llandovery during the 2015-16 season while 19-year-old flanker Evans has played for Scarlets' Under-18 side.
Both players have been included in Wales' squad for June's Junior World Championship.
Wales play Ireland, Georgia and New Zealand in Pool A in Manchester.
"They both enjoyed a very successful Six Nations campaign and will take confidence into the forthcoming World Championships," Scarlets general manager of rugby Jon Daniels said.

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Anna has started the challenge, which is a BBC Get Inspired and Public Health England's One You campaign, especially designed for people who have done little or no running.
The campaign is a nine-week plan, starting with a brisk walk and ending with a 5k run.
If you want to start your own Couch to 5K Challenge just like Anna, visit the Make Your Move website.
And you won't be on your own - choose your trainer from some familiar faces. Radio DJ Jo Whiley; comedian and actor Sanjeev Kohli; 13-time Olympic and World Championship gold medallist Michael Johnson and comedian Sarah Millican will talk you through your run and support you every step of the way.
Impress yourself. Take on the challenge.
Six teenagers found dead in a garden hut in the German state of Bavaria died from carbon monoxide poisoning, police have said.
[NEXT_CONCEPT]
Wales Under-20 Grand Slam winners Shaun Evans and Dafydd Hughes have signed their first professional contracts with Scarlets.
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Make Your Move has caught up with BBC Radio 5 live's Anna Foster, who has completed week one of the Couch to 5k Challenge.