The ground handler and airport services firm intends to cut 176 roles at Luton, where it currently employs 374 people.
Roles are spread across baggage handling, ramp agents, bus drivers, and customer service positions.
The announcement comes ahead of the furlough scheme being wound down at the end of October.
Unite said it received notice of Menzies proposals on Wednesday (16 September).
According to Unite, while Menzies is seeking candidates to volunteer, it is not offering enhanced terms, which the union said would "almost certainly" result in many compulsory redundancies.
Unite regional officer Jeff Hodge said: “Unite warned the 16 September would be a grim day for workers unless the government signalled that further jobs assistance was on its way.
"They did not, and as a result, around half of the Menzies workforce at Luton airport will lose their jobs. This is not just a hammer blow for the workers affected but for Luton itself as the sheer level of job losses at the airport is having a terrible effect on the local economy.
“The real villains are the government who first promised to provide specific support to the aviation industry in March. The promised and vitally needed support has failed to materialise.
“With the end of furlough fast approaching aviation companies, which have been the sector worst affected by the pandemic, are looking over a cliff edge and as a result job losses are increasing.
“The aviation industry is viable once Covid-19 is under control, but the industry cannot bounce back if it continues to lose jobs like these. The bottom line is that workers should not be paying with their jobs.”
Unite said it would now enter into negotiation with Menzies to mitigate job losses, seek better terms for voluntary redundancy, and ensure the process is "fair and transparent".