The incident took place Saturday afternoon, when a taxi driver got close to the convoy in western Baghdad's Atafiyah neighborhood, according to a police officer at the nearest station.
The U.S. Embassy in Baghdad corroborated that account, but said it could not confirm whether anyone was killed or wounded.
Embassy spokesman Philip T. Reeker said the company involved was DynCorp International, one of three firms contracted to protect American officials in Iraq.
"DynCorp did inform the Embassy that at 12:45 on Saturday, there had been a security incident involving a DynCorp PSD in Baghdad," Reeker said, using the acronym for private security detail.
"They reported that a private vehicle approached the convoy, and continued to approach to the point where a member of the PSD used his weapon to disable the vehicle," Reeker told reporters on a regular conference call from Baghdad.
The taxi driver was shot in the head and chest, and died at the scene, the police officer said. He spoke on condition of anonymity because he was not authorized to release the information.
Afterward, police searched the man's taxi and found no weapons nor any other evidence of suspicious activity, the officer said.
Reeker said the convoy was comprised of seven vehicles, but he would not give details about who they were carrying nor their destination.
"These are very upsetting incidents for everyone involved. DynCorp is working with the Iraqi Ministry of Interior to investigate," he said.