"Police arrested 13 people today and referred them to the (military) state security court," Maan MP Amjad al-Khattab said.
"Businesses and shops in the city stayed closed for the second day as part of civil disobedience amid a tense calm," he said without elaborating.
The unrest erupted early on Sunday as angry rioters, who torched shops and the post office, accused police of failing to arrest suspects in the killing of the two men.
Khattab has said the murders took place six days ago.
A YouTube video that "showed unknown people kicking the corpses of the two men" had fuelled people's anger, he said on Sunday.
Police said investigations were still under way, insisting that the video footage had been fabricated.
In April, armed clashes between students at Maan's King Hussein bin Talal University killed four people and wounded more than 25.