The Taliban said they had shot the helicopter down and captured 15 people.
The MI-17 helicopter owned by a private foreign company made an emergency landing in the northern province of Faryab Tuesday after it developed a technical problem, the defense ministry said.
"The insurgents then attacked and as a result two soldiers and one member of the crew were killed ... 18 people were captured," the ministry said in a statement, Reuters reported.
"Security forces have started a clearance operation to free the captives."
The Taliban, fighting to expel foreign forces and bring down the US-backed government, have made gains over the past year outside their southern and eastern heartlands and into northern areas including Faryab.
The ministry did not identify the captives or say if they were soldiers or civilians, or if any foreigners were among them. Police said Tuesday 13 government soldiers had been captured.
The Taliban said five people had been killed and they had captured 15 people who managed to get out of the burning helicopter, most of them soldiers.
"The captured people have been taken to a safe place and an investigation has started," Taliban spokesman Qari Yousuf Ahmadi said in a statement.
He made no mention of any foreigners among the captives.
A US defense official, speaking on condition of anonymity Tuesday, did not comment on the incident itself but denied claims on Twitter that any US military personnel had been captured.
The ministry did not identify the company that operates the helicopter.