Crews were called to the property in Middle Road at around 6.50pm.
A spokesman for the fire service said three appliances, one from Shoreham and two from Hove, were sent to tackle the blaze which broke out in a ground floor laundry room in the building. No-one was injured.
A CO2 extinguisher was used along with two breathing apparatus and a high pressure hose reel to tackle the flames.
A thermal imaging camera was also used to check for heat hotspots and positive pressure ventilation fan was used to remove smoke from the building.
The spokesman added crews are still in attendance but the fire has been extinguished.
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