Thousands of demonstrators have taken to the streets in the southern city of Basra, angry at pollution of the water supply which has put 30,000 people in hospital.
Seven demonstrators have been killed in clashes with security forces since Tuesday, while protestors set fire to part of the provincial government headquarters.
Sadr, whose political bloc won the largest number of seats in May elections, on Thursday called for a special parliamentary session to address protesters' concerns.
Prime Minister Haider al-Abadi, along with the ministers of interior, health, housing, water resources and electricity, must all attend along with officials from Basra province, Sadr said.
"We will be uncompromising and you have been warned, be ready," said the cleric, whose successful campaign in the May election focused on tackling Iraq's endemic corruption.
Politicians must present "radical and immediate" solutions at the meeting or step down if they fail to do so, he said.
Abadi responded shortly afterwards, saying he was "ready to attend a parliamentary session with the ministers and officials concerned, to discuss the situation and the needs of Basra province".
The premier is trying to hold onto his post in the future government through forming an alliance with Sadr, a former militia chief who has called for Iraq to have greater political independence from neighbouring Iran and the United States.
Despite Iraq holding elections nearly five months ago, parliament reconvened for the first time on Monday after claims of fraud triggered a vote recount.