Two dozen U.S. special forces were on a mission to rescue a team of military personnel when the helicopter was attacked, a U.S. official told CNN.
"It's a big loss. The numbers are high," the official said on condition of anonymity.
A statement from President Hamid Karzai's office in Kabul said the Chinook helicopter went down in the province of Warduk, CNN said.
In the statement, Karzai expressed "his sympathy and deep condolences to U.S. President Barack Obama and the family of the victims," the British broadcaster said.
NATO acknowledged the crash and said it was investigating.
The BBC said the military passengers were members of special forces who had been on a counterinsurgency mission in which eight Taliban militants were killed.
The Taliban issued a statement claiming responsibility for shooting down the helicopter.
The crash is the largest single loss of life for U.S. troops in Afghanistan since the 2001 military intervention began.
More than 2,600 U.S. soldiers have died in the conflict, Defense Department statistics show.