Thousands of jobs are at risk after the company halted plans due to rising construction costs.
Talks were held with the UK government regarding funding, but no terms were agreed.
Construction union Unite has hit out at the government over the project, calling this announcement "the latest chapter in the sorry saga of recent UK energy policy".
Unite national officer for energy Peter McIntosh said: "This government should be held to account as it has no coherent policy and has, yet again, let the country down. The lights are going out when it comes to energy policy.
"There are very real concerns over how we will keep the lights on for industry and consumers in the coming decades.
"Without Wylfa being built, there is no way the country can meet its climate change obligations which it committed to when it signed up to the Paris Agreement in 2016.
-- Advertisement --
"We need to replace the current generation of nuclear plants and Wylfa is a key part of that programme.
"Business secretary Greg Clark needs to step up to the plate and recalibrate energy policy with a vigorous commitment to substantial government funding for large-scale energy infrastructure projects."
The suspended work in Wylfa follows the withdrawal of Toshiba from the Moorside nuclear power station project in Cumbria in November.
Unite has pinpointed this and a few other occasions as factors that are leading to a crisis in UK energy policy.
Unite Wales regional secretary Peter Hughes added: "This is devastating news for the Welsh economy and, in particular, that of north west Wales. The future regeneration on the region has been based upon the bedrock that Wylfa Newydd would proceed.
"For that to now be suspended is a hammer blow to the future prospects of some of most economically deprived communities in the whole of Wales.
"Although this decision has ultimately been made by Hitachi, the UK government must take a massive share of the blame. It has failed miserably to put its full weight behind this bid and to effectively advocate the case for Wylfa Newydd.
"For the prime minister Theresa May to fail to raise Wylfa Newydd with the Japanese prime minister Shinzo Abe last week was shameful.
"The UK government's complete obsession with its disastrous Brexit strategy has meant it has completely took its eye off the ball in getting this crucial infrastructure project over the line.
"Theresa May's government is failing Wales at every turn."
(CM/JG)
