The turnover is part of an agreement with the interim Iraqi government to end fighting with U.S. and Iraqi forces in the Shiite militant stronghold.
But violence continued in other parts of Iraq on Monday, including a suicide car bombing in western Mosul that exploded as an American military convoy passed by, killing two Iraqis and wounding 18 others.
Also Monday, Al Jazeera television reported that a militant Iraqi group said it had beheaded a Turkish contractor and his Iraqi translator as punishment for working with U.S. forces in Iraq.
The station aired scenes from a video by the Army of Ansar al-Sunna group showing the Turk standing between two masked militants. Al Jazeera, which did not broadcast footage of the actual beheading, said the group killed the two men after they "confessed" to have cooperated with U.S. forces, Reuters reported.
The U.S.-backed government is working on retaking control of rebel-held areas in Iraq by political or military means ahead of national assembly elections due in January.
Members of al-Sadr's Mahdi Army began turning in their weapons for cash at the start of a five-day exchange period. The payments ranged from $5 for a hand grenade to $1,000 for a heavy-caliber machine gun, police said, according to the Associated Press.
Checkpoints were set up along the roads to three Sadr City police stations, and Iraqi National Guard members were stationed on surrounding rooftops.
Police Maj. Kadhim Salman said fighters had turned in machine guns, TNT paste, land mines and other explosives.
"God willing, there will be no more fighting and Sadr City will live in peace," said Malik Jomaa, who walked up to a station with a white bag containing two grenade launchers.
The Mahdi Army agreed over the weekend to hand in its medium and heavy weapons, and in return the government said it would start releasing detained al-Sadr followers as long as they did not commit crimes, the AP reported.
Vice President Ibrahim al-Jaafari called the arms transfer a "good and positive initiative," and said he hoped other insurgents would follow Sadr City's example.
Prime Minister Iyad Allawi's interim administration has committed more than $500 million to rebuilding Sadr City, where al-Sadr's militia has clashed for months with U.S. forces.
This is not the first time Iraqi authorities have tried to broker a peace deal with al-Sadr and his militia. An agreement aimed at ending fighting in the holy city of Najaf in August allowed the militia to leave with its weapons, but clashes continued in Sadr City.
So far, al-Sadr has not agreed to disband his Mahdi militia, a key U.S. and Iraqi demand.