Last august, al-Sadr ordered his al-Mahdi Army fighters to stand down for six months, but recently warned that he may not extend the ceasefire if raids against his supporters continued.
The US military has expressed hope that al-Sadr will extend the ceasefire but continues to target what it says are Iranian-backed breakaway factions in raids that have alienated his followers.
Iraqi police acting on a tip-off found the rockets primed for launch in the back of a truck in Obeidi in eastern Baghdad.
Explosives experts were trying to defuse the rockets when two of them detonated in quick succession.
Police confirmed that another two rockets had already been fired.
Iraqi government officials, police and medical workers said at least 27 people were wounded in the blast, but the US military gave a lower toll of three civilians killed and 17 wounded in the explosion.
A day earlier, at least five people were killed and more than a dozen wounded in a rocket attack on an Iraqi housing area near the Baghdad international airport and a nearby US military base.
Two US soldiers were also wounded in Monday's strikes, with US troops arresting six Iraqi suspects around the launch sites.
Iraqi police said the rockets were launched from Amil, a predominantly Shia neighbourhood southwest of the capital.