Up to 3,000 workers at the company's Coventry factory are set to launch a 24-hour stoppage on 27 July, followed by an all-out strike from 21 August if the dispute is not resolved.
The action follows rejection in a ballot of proposed changes to working hours which would have seen a reduction from the present 39 a week to 36 and three-quarters.
Union leaders had recommended the deal to their members but it was turned down because of concerns over compulsory Friday night shifts.
A spokesman for the company said: "We are shocked, surprised, and disappointed that action has been called after such long and thorough negotiations which went on for months and ended in acceptance by union officials."
The spokesman said the decision was a "setback" and he urged union leaders to reconsider the strikes. "We are slightly bemused. To be in this position now is bizarre, particularly when the offer was so positive for us and for the workers."
Peugeot said the proposal would have given its workers the shortest working week in British car manufacturing.
Some employees who work over the weekend would have seen their hours increase under the deal but they had been offered a pay rise of 17% to compensate, said the company.
Tony Woodley, chief negotiator for the Transport and General Workers Union, said: "Obviously I am disappointed but there were elements of the deal that were unacceptable and we cannot ignore our members' views. They voted in great measure to say no and we have now given the company some time to review its position."
The last strike at Peugeot was 22 years ago and unions had described industrial relations at the factory as a "model" for the industry.
