Qassem Allawi, a ministry spokesman, said: "American forces accompanied by Iraqi forces broke into the ministry, forced the guards to lie on the floor and took Zamili."
Nasar Al-Rubaee, head of the Sadrist bloc in the Iraqi parliament, told Al Jazeera the US action amounted to a "kidnapping" and was "unlawful and illegal because there is no warrant".
The US military said: "These militia members are reported to target Iraqi civilians using MoH [Health Ministry] facilities and services for sectarian kidnapping and murder."
Waleed al-Zamili, Hakim al-Zamili's brother and a health ministry employee, denied the accusations had anything to do with his brother.
He said: "When they arrest anyone from the Sadr movement they make these sorts of accusations."
Health ministry officials are threatening to go on strike unless al-Zamili is released, a strike that would include Baghdad's already overcrowded hospitals.
Hoda Abdel-Hamid, Al Jazeera's correspondent in Baghdad, said: "Under the current situation in Baghdad, that could have a devastating effect on the citizens."
Al-Zamili's arrest and the raid on the health ministry came as Iraqi and US troops fanned out across the capital in part of a long-awaited security crackdown.
Nuri al-Maliki, the Iraqi prime minister, has pledged to tackle both Shia and Sunni fighters in the Baghdad offensive. Critics have said previous offensives failed because he avoided going after Shia groups.
Abdel Mahdi al-Matiri, an official in Sadr's movement, said: "Zamili is in the government. Maliki should not just keep watching. Maybe tomorrow they will arrest him too."
Despite the US military's Baghdad security plan, which officials said got under way on Wednesday, violence continued in the capital city.
A car bomb in Baghdad killed six people and wounded 10 others.
"When they arrest anyone from the Sadr movement they make these sorts of accusations"
Waleed al-Zamili, Zamili's brother
The blast was reported to have occurred close to a Sunni mosque in al-Ameen, which lies in the Nissan district.
Seventeen people also died and at least 25 were wounded by a car bomb in Al-Aziziya, southeast of Baghdad.
In Baquba, northeast of Baghdad, four policemen and a civilian died during an attack on a patrol, security sources said.
The US military plan to secure Baghdad's most dangerous districts will see about 30 security stations manned by Iraqi police and army units set up and kept under 24-hour US troop surveillance.
The security stations are intended to supplement Baghdad's existing 54 Iraqi police stations.
Ten of the new security stations are already in operation, Major-General William Caldwell, a US military spokesman, said on Wednesday.
Caldwell, said: "Ten are up and running, and there's going to be at least double, if not triple, that number that will eventually be out there."
Baghdad's security plan aims to deploy up to 85,000 US and Iraqi troops on the streets.