Transferring security to Iraqi security forces is a part of British and US plans to withdraw troops from Iraq.
Muthanna would be the first of Iraq's 15 provinces outside of the relatively peaceful Kurdish north to come under full Iraqi control.
Nuri al-Maliki said: "Muthanna is the first Iraqi province that will have the honour of being transferred from multinational forces to Iraqi forces.
"The security file will be handed over completely next month and we will determine the exact date later on."
Al-Maliki made his comments hours after Des Browne, the British defence minister, arrived in Baghdad for a two-day visit.
Britain, with about 7,000 troops in Iraq, has 150 soldiers deployed in largely Shia Muthanna. Australia and Japan also have forces in the province neighbouring Saudi Arabia.
Muthanna has not seen the levels of violence that have gripped Basra province, also under British control, where there have been frequent clashes between British troops and Shia militias, prompting al-Maliki to declare a state of emergency.