The arrest was captured on camera by international photojournalists.
Asked on Tuesday why the man had been arrested and put into the back of a Humvee vehicle on Tahrir Square, the commanding officer told Reuters at the scene: "This man has been detained for making anti-coalition statements."
He refused to say what the man said.
Another US soldier swore at Iraqis as he ordered them to move back. School teachers and young students looked on.
The troops had earlier closed off the sprawling square with barbed wire to search for home-made bombs, which along with rocket-propelled grenades have killed 153 US soldiers since combat was declared over on 1 May.
A US military spokesman said he had no immediate information on the incident.