Six fire engines were called to reports of a fire at Guildbourne Court, Guildbourne Centre, Worthing, at 7.54pm on Saturday.
Fire crews used one hose reel to help contain the fire, according to a spokesman.
Two people who were in the building when the fire broke out were led to safety by fire crews.
A spokesman for WSFRS said: “One person had to be checked over by ambulance crews.
“Three pieces of breathing apparatus were used at the scene.”
Fire crews left the scene at 9.39pm.
The cause of the fire is currently being investigated by Sussex Police.
A spokesman for Sussex Police said the investigation is ‘ongoing’.