The decision follows an attack on a government office in south Baghdad late last month that killed three people, including a policeman, and which the authorities blamed on the group.
Like other armed groups trained by Iran during the war against the jihadist Islamic State group (IS), the Hezbollah Brigades were integrated into the regular security forces as part of the Hashed al-Shaabi (Popular Mobilisation) force.
However, the faction has developed a reputation for sometimes acting on its own.
Iraq's Joint Operations Command previously said that more than a dozen suspects were detained over the July 27 attack on an agriculture ministry office, which was prompted by the sacking of the director.
Saturday's government statement said the suspects were "fighters belonging to Hezbollah Brigades and affiliated to Regiments 45 and 46 of the Hashed al-Shaabi".
It charged that the attack on the ministry's office had been led by the former director.
"In addition to being implicated in several cases of corruption", the suspected ringleader stood accused of "falsifying official documents, certificates and contracts so that farmland could be confiscated from its legitimate owners", the statement said.
The government said it regretted "command and control failings within the Hashed al-Shaabi" and condemned the "presence of armed factions which do not respect military rules and procedures".
The authorities announced the "dismissal of the commanders of Regiments 45 and 46" and the prosecution of "everybody implicated" in the case.
A security official speaking on condition of anonymity said 25 people faced trial -- the Hezbollah Brigades fighters and the former head of the ministry office.
The group says many of those detained had nothing to do with last month's clash.
The case comes amid deep divisions in Iraq over a proposed law that would further formalise the role -- and perhaps, the autonomy -- of the Hashed al-Shaabi.
US Secretary of State Marco Rubio has said the proposed legislation "would institutionalise Iranian influence and armed terrorist groups undermining Iraq's sovereignty".
Formed in 2014 when Iraqis were urged to take up arms against IS, the Hashed now counts more than 200,000 fighters and employees, and wields major military and political clout.
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