The shutdown of the power station comes after workers identified damaged pipe recently but the plant is expected to restart operations in two weeks, BBC News reported.
The station comprises two 490MW Magnox nuclear reactors while the first reactor was closed for maintenance work in January 2014.
BBC News cited a Wylfa spokesman as saying that no radioactive material has been involved in the incidents.
Workers tried to resume the operation of the first reactor and discovered that repairs were required to one of the turbines and a gas circulator, further delaying to the reactor start-up.
The power station, once resumed, would continue to produce energy until the 30 September, with a possible extension to December 2015 upon passing of safety checks.
The second reactor at Wylfa plant was retired in 2012 following completion of 41 years of service.
