The huge plumes of smoke from the fire is visible for miles.
The Scottish Fire and Rescue Service was called to the scene at Mossbell Road shortly after 8am on Friday.
No casualties have been reported at the site run by Tradebe Healthcare and people have been warned to avoid the area.
Tradebe confirmed a fire broke out inside its facility at around 8am but said "it is too early to speculate as to the cause".
Extra fire engines were sent out and a total of nine fire engines plus two aerial rescue pumps were sent to the scene.
A Scottish Fire and Rescue Service spokesperson said: “We were alerted at 8.11am on Friday, July 9 to reports of a building on fire at Mossbell Road, Bellshill.
“Operations Control mobilised four appliances to the scene where a fire is affecting an industrial unit.
“Additional responses have been sent to the area and there are currently nine appliances and two aerial rescue pumps in attendance, and firefighters are continuing to tackle the fire.
“There are no reported casualties at this time.”
Police are urging the public to avoid the area as the industrial estate is currently closed.
The purpose-built site opened in December 2019 and can treat up to 80 tonnes of medical waste per day using "state of the art technology", the firm has said.
Spanish-owned Tradebe Healthcare runs the £10 million per year contract to remove waste from hospitals, pharmacies, GP surgeries and dental practices across Scotland.
Gordon Beattie, director of national procurement at NHS National Services Scotland (NSS), said: "NSS is aware of the fire at a facility operated by our clinical waste partner Tradebe.
"Tradebe have kept us fully informed and we are working in partnership to ensure that their alternative arrangements are in place to protect service."
A Tradebe spokeswoman said: "An incident occurred today at approximately 8am on the Tradebe site at Bellshill when a fire broke out inside our facility.
"All Tradebe colleagues were safely evacuated and everyone is accounted for.
"At this stage we are collating all the available information on the incident and it is too early to speculate as to the cause."