The rise in water level has prompted authorities to issue an alert for villages along the river's banks in Narmada, Bharuch and Vadodara districts.
Heavy showers lashed several areas of Saurashtra and south Gujarat on Wednesday, officials said, adding that the state has so far received 116.59 per cent of the season's average annual rainfall.
Heavy rains in Gujarat in the past few weeks have created havoc in the state due to flooding in several parts of the state.
Around 25,000 people have been rescued since the floods hit putting all security forces into immediate action.
The mother, with her new born twins and an attendant, were instantaneously put into the aircraft and flown out to safety with due care.