The men pulled up in 15 four-wheel-drive vehicles and kidnapped employees and customers at an office on a street in Arasat al-Hindiya, once a thriving commercial district and upmarket residential neighbourhood.
Some witnesses said the offices were those of the Iraqi-American Chamber of Commerce and Industry and al-Rawi mobile telephone company.
A witness who refused to reveal his identity said: "I was on the first floor of the Iraqi-American Chamber of Commerce and they took all the men downstairs. They were in camouflage army uniforms. They handcuffed the men and blindfolded them.
"Me and five others were left behind because all the cars were full."
Police said that the head of the chamber and 11 employees were among the kidnapped. The chamber is an organisation that represents companies seeking to boost trade between post-war Iraq and firms in the United States.
Another witness said: "Two gunmen stayed outside and the others entered the building. They dragged the employees and put them in the cars."
George Bush, the US president, and Nuri al-Maliki, the Iraqi prime minister, have agreed to send thousands more troops to tackle "sectarian and insurgent violence" in Baghdad.
A previous crackdown by al-Maliki has failed to ease communal violence which has raised fears of civil war.
More and more neighbourhoods are being carved up along sectarian lines in the capital, once a melting pot of Iraq's sects and ethnic groups. More and more shops and businesses are closing.
Officials have acknowleged that sectarian militias and anti-US fighters have infiltrated security forces.
Iraq's military leaders said in a statement on Monday: "Joining the military and implementing national obligations need loyalty and people should discard party, sectarian and racial affiliations and stay away from politicising the army."
In typical bloodshed in Baghdad, assailants killed Fakhri Salman, a brigadier in the Iraqi National Intelligence Service, an interior ministry source said.
Maad Jihad, an adviser to the health minister, was also killed in the Mansour district, the source said.