The German aircraft - part of the International Security Assistance Force (Isaf) - crashed into an empty house, where there were two Afghan girls.
"
There was no explosion beforehand, no missile exchange or anything like that
"
Isaf spokesman
German Defence Minister Peter Struck said the children were missing - unconfirmed reports say they were killed.
The cause of the crash is unclear - Mr Struck said "there were no indications whatsoever of shots fired".
'Accident'
The Sikorsky helicopter nose-dived out of the sky with flames coming from the engine.
"There were seven crew members on board, members of the German Isaf contingent, all of whom were killed," Mr Struck told reporters in Berlin.
"The helicopter was conducting a routine flight. We are doing everything to determine without delays or gaps the cause of the accident," he said.
Earlier, Kabul Police Chief Bashir Salangi said two children on the ground had died.
"I actually saw the incident. I saw the helicopter get into difficulties with smoke and flames coming from the engine compartment just before it crashed," Isaf spokesman Gordon Mackenzie said.
He said the helicopter had not been fired upon.
German Chancellor Gerhard Schroeder said he was shaken by the crash.
"Even though everything indicates that this was a terrible accident, this accident makes it tragically clear... that the army's mission in Afghanistan is a difficult and dangerous operation," Mr Schroeder said in a statement.
The German air force provides surveillance and assistance to peacekeeping troops on the ground.
US soldier dies
The crash came hours after a US soldier died after clashes with enemy forces - the first US fatality in a confrontation in Afghanistan for seven months.
His unit came under fire while on early-morning patrol in Paktika, a border province with Pakistan.
He died while undergoing surgery.
The 4,800-strong Isaf was deployed in Kabul at the end of last year to help the interim government maintain security in the city and its outskirts.
Turkey took over leadership of the force in June 2002.