They said the woman seemed wracked with remorse over the shooting of Joseph Griffin, 49.
They added that she held an Iranian passport but offered no evidence that Iran may have orchestrated the attack.
She arrived at police headquarters and headed to a bathroom where she loaded a pistol and hid it under her long scarf, they said. She then approached the American police trainer as he was walking to a canteen and shot him.
It appeared to be the first time that a female member of Afghanistan's security forces had carried out such an attack.
A police official said: "This was a very organised shooting. There must have been bigger hands involved. At this stage, we can only say that she could have been brainwashed either by the Taliban or al Qaeda."