Al-Sadr is wanted for the 10 April 2003 assassination of rival cleric Abd al-Majid al-Khoei, a charge he denies, who was stabbed to death in the central Shia city of Najaf, along with two other people.
He is also wanted for questioning over the deaths four months ago of three people, including a pregnant woman, the source said.
In a third case, al-Sadr is accused of confiscating the "khums", or donations from worshippers to mosques and shrines in the south, worth a few hundred dollars.
The official said an arrest warrant was signed and delivered by an Iraqi judge in August.
US Brigadier General Mark Kimmitt told reporters: "We believe it is an internal matter.
"This was a warrant issued by an Iraqi judge. It will be carried out by Iraqi police forces, he will be detained in an Iraqi jail and he will be prosecuted by an Iraqi judge," he said.
The occupation, he said: "Will be coming to help, if and when specific requests for assistance are made".
The legal adviser also said the occupation authorities would "provide logistic and security help if the Iraqi authorities request it."
He said Iraqi judges were in possession of evidence to support their claims.
Al-Sadr is wanted for the murder
of Abd al-Majid al-Khoei (R)
"Everything is ready for al-Sadr's accusation," he said.
But he declined to say when and how the warrant would be served.
"Obviously he has to be arrested and it could take a number of weeks, but the warrant will be executed," he said.
He said the announcement about the warrant, while al-Sadr's supporters are rising up against the US-led occupation forces, was not a coincidence.
"The events of the past week have made it necessary to announce it. It has been announced now so that all the people of Iraq understand that Muqtada al-Sadr is not a hero, a great religious leader or a man of peace, but a criminal and a thief."
A message to the Kuwaitis
On Wednesday, al-Sadr called on the Kuwaitis to expel the US military base from their land.
"I call on our neighbour Kuwait to ask that American and other bases be removed so that this state may stand hand in hand with us to remove the big nightmare and great Satan from Iraq, whose people are suffering from the occupation," Sadr said in a statement made available to Aljazeera.
"You cannot keep silent about these crimes and you must help your brothers by removing terrorism from your land," said the statement written in Arabic.
It said Kuwait, which borders Iraq to the south, no longer needed US troops now that Saddam Hussein had been ousted.
Around 25,000 US troops are stationed in Kuwait, a key US ally, but their number can fluctuate with rotation of troops from Iraq. Kuwait also hosts other occupation forces involved in Iraq.