In a statement read by al-Ubaidi on Thursday, al-Sadr said: "Any member of the Mahdi Army who conducts violent acts during the ceasefire, the Sadr office declares they will no longer be part of the Mahdi Army."
He said al-Sadr had issued the statement in response to rumours that the ceasefire was about to come to an end.
Al-Ubaidi, a senior al-Sadr official in the southern city of Najaf, declined to comment on whether the ceasefire would be extended.
The Iraqi police said Mahdi Army fighters had clashed with Iraqi and US soldiers in Sadr City - a poor and pre-dominantly Shia neighbourhood northeast of the capital, Baghdad.
Police said three people, including a woman and a child, were hurt in the clashes and 16 people had been detained.
A US military spokesman said one person was killed and another was injured when US and Iraqi soldiers conducted raids "targeting criminal elements".
Al-Sadr, who led two uprisings against US forces in 2004, ordered the Mahdi Army to observe the ceasefire so he could reorganise the splintered force.
His fighters had been involved in clashes with US troops and Sunni groups, and the Pentagon once described it as the greatest single threat to peace in Iraq - a term it now uses to describe al-Qaeda.
Earlier this week al-Ubaidi said al-Sadr has been gauging the mood among senior figures about the ceasefire.
Recent statements from al-Sadr's camp have indicated a growing unease about the truce, with members claiming they are being targeted by Iraqi security forces.
US commanders have said they are confident that al-Sadr, the son of a revered Shia cleric killed under Saddam Hussein, would extend the freeze, although US and Iraqi forces continue to target "rogue" Mahdi Army units.