"There were three killed and eight wounded," in the clashes which ended early on Sunday, said Dr Wisam Khalid, who is based at the hospital in Amara, 365km from Baghdad.
Fifteen other supporters of al-Sadr were detained.
A spokesman for al-Sadr said on Saturday a member of his Mahdi Army had been killed in Amara and another injured as they tried to stop a British patrol searching homes in the city.
Quoting a source at al-Sadr's office in Najaf, Aljazeera's correspondent said Iraqi fighters in the city attacked a British military convoy, causing casualties among the soldiers.
Riots erupted after the attack, but al-Sadr's Mahdi Army controlled the situation after the withdrawal of the British forces, reported the correspondent.
Police and witnesses also said there had been attacks on two US convoys around the city on Saturday, with at least one vehicle damaged.
Other reports said mortar bombs and grenades were also fired overnight at US occupation forces in the town of Najaf in southern Iraq, witnesses said on Sunday.
US troops killed
There were no reports of casualties in the attack, which also targeted the city's US-led occupation administration office.
Al-Sadr remains holed up in the city of Najaf where he is wanted over the murder of a Shia cleric last year and US forces have vowed to "kill or capture" him.
Also on Sunday, four US occupation soldiers and two members of the Iraqi security forces have been killed in separate attacks in Baghdad and near the southern city of Amara.
Two US soldiers and two members of the Iraqi Civil Defence Corps were killed in north-west Baghdad, a senior military official said.
Two more US troops were killed near Amara on Saturday when their convoy came under fire from small arms and a rocket-propelled grenade.