Some 25% of the building was damaged by fire and heat while the rest of the business was damaged by smoke, according to a spokeswoman for West Sussex Fire and Rescue.
Four fire crews with 14 firemen were called out to the Stephenson Way-based business at 2.50am on 13 April, and the fire was put out at 5.56am.
The spokeswoman said: "The fire is understood to be accidental, but there has been some damage to the single-story building. No one was hurt."
Lee Simmonds, partner at Swift Printers, said: "We are already putting in place several measures to ensure a continued service for our customers.
"We expect to be up and running with business as usual within the next week."