The fire broke out at about 10pm on Tuesday, on the site on the Holyhead Road in the centre of the town, sending flames leaping into the sky.
No-one was hurt in the blaze.
Firefighters from across the region including Oswestry went to the scene along with the police and ambulance service.
The fire is believed to have been confined to one of the towers at the factory.
No-one was evacuated from the plant, which employs 600 people.
A North Wales Fire Service spokesman said the cause was possibly related to a transformer unit.
Fire crews from Chirk, Llangollen, Johnstown and Oswestry and the aerial ladder platform from Wrexham were on the scene. It took two-and-a-half hours to deal with the fire.
Kronospan makes medium density fibreboard.
Residents posted photos of the fire on Facebook and social media, many worried about the safety of employees.
They also praised local firefighters, who have spent hundreds of hours over the last fortnight dealing with the mountain fires above Llangollen.
Councillor Terry Evans who represents Chirk on Wrexham Borough Council said he was concerned about any pollution from the fire and said he would be speaking to environmental health officers.