More than 20 people have also been wounded during the fighting, officials said.
The fighting is the most severe seen in central Baghdad since US and Iraqi forces, aided by Sahwa loyalists, battled against al-Qaeda-linked fighters in 2007.
The clashes in Fadhil came after Iraqi forces arrested Mashhadani on Saturday, Iraq's interior ministry said.
Mashhadani was detained over allegations of murder and extortion and "violating the constitution", major general Qasim Atta, Baghdad’s military command spokesman, said.
"We also have information that Mashhadani heads the military branch in Fadel of the [banned] Baath party [of Saddam Hussein, the executed former Iraqi president], Atta said.
Iraqi troops "are not hunting-down the Sahwas but carrying out a search operation for suspects wanted by the judicial authorities and gangsters who are firing on our forces," Atta said.
While Mashhadani helped Iraqi and US troops force al-Qaeda from the Fadhil district, he is accused of turning the area into his own stronghold.
Iraq’s Shia-Muslim-led government, which has in the past expressed concerns over the Sahwa fighters' long-term aims, has said that 20 percent of all Sahwas will be integrated into the Iraqi security forces.