The announcement was made by the minister of state for Urban Development Bhaskar Jadhav in the Legislative Council.
"The inquiry would be completed within two months," Jadhav said.
Earlier, taking note of the irregularities in awarding contracts to private players by Brihanmumbai Municipal Corporation, Davkhare told Jadhav that the state government could go ahead with the CID probe.
Congress member Bhai Jagtap, his NCP counterpart Kiran Pawaskar among others had raised the issue through a calling attention motion.
Pawaskar also alleged that despite the state government having spent Rs 950 crore towards widening the bed of Mithi river among other works, no concrete improvement was seen in the condition of the river.
The river flows for a total of 15 km before it meets the Arabian Sea at Mahim Creek in the island city.
The Leader of Opposition Vinod Tawade also demanded an inquiry against both BMC and the Mumbai Metropolitan Region Development Authority (MMRDA), the nodal agencies for the Mithi river project.