At its height, 10 pumps were called to the scene and 70 firefighters were involved.
Kent Fire and Rescue Services were alerted to the incident at the recycled containerboard plant at 17.30 yesterday evening.
The fire is understood to have started in a waste compactor and has affected 500 tonnes of baled paper.
A spokesman for Smurfit Kappa said nobody was injured and the fire had been extinguished.
He said: "There is a small amount of raw material damage, but there has been no damage to equipment. Production at the site has been minimally affected."
The fire brigade was still at the scene of the fire at 8:00am this morning. However, at 11:30 last night it reported that good progress had been made tackling the blaze.
Smurfit Kappa operates in 30 countries and produces containerboard, solid board, and corrugated and solid board packaging. It has annual sales of €7bn (£5.5bn) and employs more than 40,000 staff.
Fire breaks out at Smurfit Kappa's Kent mill
Firefighters have been working through the night to stop a blaze at Smurfit Kappa's Snodland mill in Kent.