Residents of these villages have been asked not to venture near the Narmada river bed, officials said.
As the Sardar Sarovar dam level rose due to inflow following heavy rainfall in the catchment areas upstream and release of water from the Omkareshwar dam in neighbouring MP, authorities opened nine radial gates of the Gujarat-based reservoir by 1.50 metres, they said.
The Sardar Sarovar dam recorded a level of 134.75 metres on Sunday morning as against the full reservoir level of 138.68 metres, an official from the Sardar Sarovar Narmada Nigam Limited said.
The dam's water level rose by 3.5 metres in the last 24 hours, he said.
"A total of 1,35,000 cusecs (cubic foot per second) of water will be released in the Narmada river through the River Bed Power House (RBPH) that produces hydroelectricity, and the opening of nine radial gates of the Sardar Sarovar dam," an official statement said.
Vadodara's in-charge collector Mamata Hirpara said authorities were maintaining a vigil and precautionary measures have been taken in 25 villages under Shinor, Dabhoi and Karajan talukas of the district.
These villages are located along the Narmada river banks in Vadodara district, and local administration has been instructed to keep an eye on the situation and take precautionary measures, she said.
Keeping in mind the possibility of more water release from the Narmada dam upstream, the district administration has appealed to residents of the 25 villages not to venture near the river bed, the collector said.
The district administration is taking all measures to avoid any accident or casualty in low-lying areas of the Sardar Sarovar dam, she added.
The Sardar Sarovar project is one of the largest water resources project in India covering four major states - Maharashtra, MP, Gujarat and Rajasthan.
The dam's spillway discharging capacity (30.7 lakh cusecs) would be third highest in the world, as per the project website.
Rains continued in parts of south and central Gujarat districts in the last 24 hours, with the state receiving 70.35 per cent of the annual average rainfall.
Kutch, Saurashtra and south Gujarat regions have received 87.35, 78.73 and 83.96 per cent of the annual average rainfall, respectively, the State Emergency Operation Centre (SEOC) said.
As against this, the north and east Gujarat regions have received 52.67 and 53.90 per cent of the annual average rainfall, respectively, the SEOC added.