More than 300 firefighters attended the fire, which broke out on the mill's paper machine 2 (PM2) on 20 December. The mill was forced to shut down and evacuate its staff.
Sappi estimates that coated paper production will be restarted early in the new year, while activities to restart the mill's uncoated paper production line (PM1) were under way on 21 December.
Other production areas, including the mill's sheeting department, stocks, finished goods, and pulp mill have not been affected.
The cause of the fire and the extent of the damage to the PM2 and coating equipment are being investigated.
Stockstadt mill's PM2 produces 230,000 tonnes of coated woodfree paper, while its PM1 produces 200,000 tonnes of uncoated woodfree paper annually.
Sappi said that no interruptions to customer deliveries were anticipated as other mills would be able to cover any shortfall while Stockstadt was out of action.