The Press Trust of India quoted officials as saying the Narmada Valley dam began overflowing on Wednesday after heavy rain in its catchment area in neighbouring Madhya Pradesh state.
"We have evacuated 847 people from Khalafiya and Sarfuddin villages," said Rajiv Topno, administrator of Bharuch district in Gujarat.
"There is a possibility of the Narmada crossing the danger mark if rains continue in Madhya Pradesh. We are keeping a close watch on the situation," he added.
The controversial Narmada Valley project includes 3,000 dams to be built across three states on the Narmada river and its tributaries. Critics say the human cost and environmental risks far outweigh the proposed benefits.