Prys Morgan from Welsh Country Foods says it's been a difficult day for staff at the Anglesey site.
Unite has pledged to work "strenuously" to see if the 350 jobs under threat at Welsh Country Foods can be saved.
Unite national officer, Julia Long described the announcement as "desperately sad news" and said the knock-on effect for the local economy could be "severe."
Ieuan Wyn Jones AM for Ynys Môn has described the news that 350 jobs are at risk on Anglesey as a "massive blow" to the local workforce and the island's economy.
The former leader of Plaid Cymru says he will be raising the issue with the Deputy Minister for Agriculture Alun Davies AM in the Assembly early next week.
350 jobs are at risk at a food company in Anglesey
The Welsh Country Foods has announced that it could be forced to close its lamb processing business after its key customer decided to go elsewhere.
The company says it's started a 90-day consultation exercise with its unions and workers.
Jose Peralta, Managing Director of VION’s red meat business, said: “This is an extremely difficult day for everyone at Welsh Country Foods following the decision by its key customer to de-list Welsh Country Foods as a supplier.
We recognise the impact which this decision will have on the local economy and the community in Anglesey and we are currently in discussions with the retailer to establish if their decision can be overturned and if any steps can be taken to mitigate their decision.
"Throughout the consultation process we will explore every opportunity to limit any potential job losses which will include attracting new customers to the site or the sale of the business to any interested parties.
"We will also work with our farmer supply base to minimise any impact that this may have on their activities."
The plant was purchased by VION Food Group in August 2008. Welsh Country Foods is the major processing facility for Welsh lamb in north Wales, handling 640,000 lambs every year.
Jose Peralta added: “If the consultation exercise does not reveal a viable way forward for this plant regrettably we will have no other option but to close the site."