Asadi said the details of the operation would be announced at a press conference.
Nuri al-Maliki, the Iraqi prime minister, had given a four-day deadline to Shia militiamen in Maysan and in its capital Amara to lay down their arms which expired on Wednesday.
Dozens of Shia militiamen surrendered to Iraqi forces hours before the deadline and police also recovered hundreds of landmines.
US commanders say Maysan has become a major centre for arms smuggling into Iraq from Iran just over the border.
The crackdown is the latest stage of al-Maliki's drive to wrest control of areas in Iraq.
The operation follows a similar crackdown launched by al-Maliki against Shia militia in the main southern city and oil hub of Basra in March.