WR Refrigeration, which is headquartered in Leicester, was served with a winding up petition by HMRC this month and yesterday announced it had gone into administration.
Nationally, 600 jobs are under threat - 59 of them at the firm's site in East Kilbride's Kelvin Industrial Area.
Administrators PricewaterhouseCoopers said the firm faces a real risk of closure.
Linda Fabiani, MSP for East Kilbride, said it was another blow for the town, which has suffered a string of jobs setbacks in recent years.
She added: "This news is obviously worrying for all workers involved.
"My thoughts are with employees.
"This is another blow to East Kilbride."
The firm also has sites in Belfast, Ipswich, Weston Super Mare, Dartford, Leeds and Wales.
WR Refrigeration had been experiencing cash-flow and trading problems and administrators were called in after it was unable to find extra funding.
Joint administrator Eddie Williams, from PwC, said: "The business faces the real risk of imminent closure."
Last year aerospace giant Rolls Royce announce it was moving its 600-strong East Kilbride workforce to Renfrewshire.