RNA - Sadr’s call came hours after President Barham Salih named Mohammed Tawfiq Allawi as prime minister in an effort to end the political tensions.
The cleric on Sunday urged his unarmed supporters to work with authorities to ensure schools and businesses can operate normally again.
In a message issued on Twitter, Sadr said "I advise the security forces to stop anyone from cutting off roads and the ministry of education should punish those who obstruct regular working hours, be they students, teachers or others."
Allawi was named as part of a deal between Sadr and rival political groups, who have wrangled since November's resignation of premier Adel Abdul Mahdi in the face of mounting unrest and protest against corruption in Iraq.
Sadr had endorsed the designation of Allawi, a technocrat, as prime minister, saying it is a good step after months of political turmoil.
Allawi must form a government within a month and face a confidence vote in parliament.
Sadr said in a tweet on Saturday that President Salih’s appointment of Allawi as Iraq’s designate prime minister could draw the support of people who have been demanding change in the way the country is governed.
“I hope the president’s appointment of Mohammad Allawi is acceptable to the people and that they have patience,” read part of Sadr’s Arabic statement on Twitter, adding, “This is a good step.”
Iraqi protesters have regularly blocked main roads in Baghdad and southern Iraq since demonstrations erupted in October. They called for creation of better jobs and services.
Sadr's supporters had previously bolstered the protesters as many of his supporters shared the same grievances as many Iraqis over a lack of job opportunities, poor healthcare and education.
Some of Sadr's followers appeared to have helped to clear out protest areas at Tahrir Square in Baghdad, the site at the heart of protest, overnight.
Allawi, the son of a wealthy Iraqi industrialist who educated at the American university of Beirut, is a cousin of pro-Western Shia politician Ayad Allawi, a figure who has been at the heart of many political disputes in Iraq for the past years.
Allawi has a reputation of repeatedly clashing with Nouri Maliki, a key political figure known for his anti-American positions who led two governments in Iraq after the US invasion of 2003.
However, the new PM designate said on Saturday that he would try to maintain his political independence as a head of government and would oppose any external pressure for appointment of ministers in his new cabinet.