EDF said the anonymous phone call was made at 0355 GMT April 30 and that, while searches continued, the core areas of the plant had been secured.
The nuclear plant was still functioning, EDF added.
The local authorities said the phone call warning had been made from a phone box in the town of Chinon in the Indre-et-Loire department.
"The police force was on the site at 0700 GMT and the bomb-disposal experts with dogs arrived on site at 0900 GMT," a local authority spokeswoman said.
The Chinon plant, which has four 900-megawatt nuclear reactors, supplies electricity to around 6 percent of the French population.
Workers at the Chinon plant have been carrying out protests in the last few months. Unions, demanding a five percent pay rise and a 1,500-euro bonus, have called for more protests.
Actions have included power capacity cuts and delaying a maintenance program scheduled to start this month.
"The bomb scare has nothing to do with the protest currently underway and we are awaiting for light to be shed on the matter," a CGT spokesman told Reuters.