The fire at the plant on Barony Road, Mountfield, broke out at about 4:15am this morning.
The Northern Ireland Fire and Rescue Service has asked members of the public to avoid the area and keep roads clear for emergency services.
A Northern Ireland Fire & Rescue Service (NIFRS) Spokesperson said: "Over 50 firefighters and officers are currently on scene with local stations being assisted by crews from Armagh and Portadown who are providing specialist appliances including a water tanker, aerial appliance and high volume pump to assist in operations.
"Crews were first alerted at 4.15 this morning and firefighting operations are still ongoing.
"NIFRS crews are working closely with the site management to minimise risk to people and the environment and it is anticipated that the incident will continue for some time."
The Fire and Rescue Service has advised the public to avoid the area in order to minimize congestion and allow on-coming emergency vehicles unhindered access.