Several hundred Iraqi troops barged into the one-storey building on Monday and conducted room-to-room searches, cuffing at least 50 men inside.
About half of them were later released.
"All the hospital staff and doctors have been arrested," said a doctor at the hospital, Ahmad Ghanim.
"We are now in a very small and poorly-equipped alternative clinic. We are only four to five doctors with five assistants," Ghanim said on Monday.
The doctor added that US forces had grounded all ambulances and fired on and disabled the hospital's only car. Doctors were also running short of medicines.
Interim Iraqi Prime Minister Iyad Allawi said 38 fighters had been killed in the operation to seize the hospital but US military sources disputed this and said 42 fighters had been killed throughout the city.
They reported no deaths at the hospital.
Allawi said 38 fighters had been
killed in the operation
They met little resistance except for a roadside bomb that
exploded close to a US military vehicle, wounding a marine.
The hospital, the largest in the city, is located on the western side of the banks of the Euphrates, which separates it from the city centre, leaving just small clinics to deal with any local wounded.
The hospital director said earlier that the facility was surrounded.
"They are telling us over loudspeakers that if we leave the building, we will be shot at," Dr Salih al-Isawi said, adding that an ambulance that tried to exit the facility was fired at.
It was not immediately clear if the driver was killed or wounded.
Al-Dulaimi said Falluja's general hospital had been undefended as it lay outside the city. "US forces have entered the hospital as it is not guarded; only doctors and patients are there," he said.
A US commander said marines also took control of two bridges in the south-west of Falluja, spanning the Euphrates, while a large, white observation balloon was seen hovering above.