US military spokesman Dan Senor said on Monday the arrest warrant had been issued several months ago for the assassination of Ayat Allah Abd al-Majid al-Khoei last year.
Asked when al-Sadr would be arrested, Senor said: "There will be no advance warning."
In subsequent clashes with al-Sadr's followers, at least five people were killed and several wounded on Monday night after US helicopter gunships bombarded al-Sadr's offices in Baghdad, where his supporters had barricaded themselves.
Two Apache helicopters attacked the offices in al-Shula district of the capital as US-led forces across Iraq confronted angry followers of the Shia leader, in addition to continuing operations against resistance fighters.
Clashes have also been taking place between occupation troops and Iraqi militiamen in the city's al-Azamiya district, which has been surrounded by US tanks with helicopters flying overhead.
One of al-Sadr's senior aides was detained on Saturday in relation to the al-Khoei assassination - provoking protests from his supporters that led to clashes with occupation troops.
Another aide insisted al-Sadr would never be captured.
"He will not be arrested; we will not allow his arrest, not by the Americans, not by the British and not by anyone else," Hazim al-Araji, director of al-Sadr's office in Kadhimiya, a Shia district of the capital, told AFP.
Al-Sadr commands strong support among his followers, especially the urban poor in Baghdad, who rally to his anti-occupation rhetoric and promises that Shia, once oppressed by Saddam Hussein, will come to dominate Iraq.
Al-Khoei was hacked to death at a Najaf mosque in April 2003 by a mob which also killed one of his aides. Senior leaders at the time blamed the killings on a group linked to al-Sadr. Al-Sadr's group has denied the charge.
After months of ignoring al-Sadr, whose influence was thought to be waning, US officials recently accused him of inciting violence, and shut down his newspaper in Baghdad last week.
Occupation forces then detained al-Sadr's aide Mustafa Yacubi at his Najaf home on Saturday. His detention stoked anti-American demonstrations across Iraq, many of which turned violent.