The woman, who was later arrested, killed the American Monday at the Kabul police headquarters in an apparent insider attack. The victim was reported to be a contractor working as police adviser.
The 33-year-old attacker was identified only as Nargis, the BBC reported, quoting Afghan authorities.
An Interior Ministry spokesman told reporters an Iranian passport and Iranian national card were obtained from her home, the BBC reported.
"Our investigation shows that Nargis is an Iranian national. After her marriage to ... an Afghan, she managed to obtain an Afghan ID illegally and joined the police," the spokesman told reporters.
Authorities were quoted as saying the woman came to the police headquarters, asking to meet the police chief, Kabul governor or the head of the criminal investigation department. When she could not meet any of the officials, she came to the canteen, where she fired one bullet at the victim and later fired at officers trying to arrest her, the report said.
The mother of three suffered "from a psychological instability," the spokesman said, adding she remained in custody while the investigation continued, the BBC reported.
The likelihood of her having been in contact with "terrorist networks" was also being investigated. If the shooting is established as an insider attack, which has become a major threat to U.S. and NATO forces in Afghanistan, it would be the first such by a woman.
Earlier, The Washington Post quoted an official that the American was shot in his heart and he died quickly in a hospital. The attacker had been identified as one of the 1,850 female police officers trained in the country since 2002.
The incident comes despite the Afghan government's claims of tough measures to verify the background of all candidates applying to join the security forces.
On the same day, five local policemen were killed by another officer in northern Afghanistan.
Insider attacks, either by members of the Afghan security forces or by insurgents posing as members, have become a major threat for the U.S. and NATO forces in the country with more than 50 coalition forces already killed in such attacks this year.