The protesters allege that the families affected by the rising water level after the closure of the gates of the dam on the Narmada river in neighbouring Gujarat have not been fully rehabilitated or compensation paid to them.
The "Jal Satyagaraha" protest began on Friday on the banks of the Narmada river at Chota Barda village in Dhar where the water level is gradually rising.
Ms Patkar, the Narmada Bachao Aandolan founder, alleged that the BJP government was ignoring the plight of the affected families and making grand plans for Modi's 67th birthday celebration when he dedicates the dam to the nation.
"People will drown in the Narmada river but they will not move. Planning is being done for the massacre of thousands of families so as to celebrate Modi's birthday with great pomp and show," said Patkar.
"This will be one of the worst days in the country".
With the water level of the Sardar Sarovar Dam steadily rising, it is speculated that one town and 192 villages in the region besides Barwani will be submerged under water. Despite the fear, people have not left their homes in the affected villages.