Black smoke which was seen pouring from the roof of the old south wing prompted numerous people to phone the emergency services at about 8.04am.
Gary Towson, from West Sussex Fire and Rescue Service, said: "The fire alarm of the hospital sounded just after 8am.
"A fire had started in the first floor staff canteen area inside the building which has scaffolding on it at the front of the hospital.
"On route to the hospital fire crews from could see black smoke pouring from the hospital site which made us think the fire was a lot worse than it actually turned out to be."
The fire was quickly extinguished and was not able to spread into the main hospital as the buildings are separate.
Some people who were working inside the old south wing were evacuated.
Mr Towson added: "There is damage to the kitchen area and some extensive smoke-logging throughout. There is also some superficial damage to the roof."
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