The Chinook helicopter went down in the eastern province of Konar while carrying troops, the statement said.
The cause of the crash was not known, nor was the fate of the passengers. A Chinook helicopter can carry up to 54 passengers plus a crew of four.
The military said the aircraft had been participating in an anti-guerrilla operation. It was the second US Chinook to crash in the country this year.
The BBC's Andrew North in Kabul says it appears that this incident is "more serious" than the previous crash.
Eighteen people were killed in that crash, which took place during a sandstorm in April.
The special rapporteur on torture Manfred Nowak said the accusations were rumours at this stage, but urged the US to co-operate in an investigation.
...He told the BBC there were a number of allegations from reliable sources that the US was holding terrorist suspects in secret places of detention, including vessels abroad.
He said that according to the reports, the ships were believed to be in the Indian Ocean.