Emergency services were called to the Mermaid Care Home, in Brighton Road, at 8.39pm,
All the residents were safely evacuated but damage was caused to a room in the home.
Police said a 56-year-old man from Lancing was arrested on suspicion of arson with intent to endanger life. He remains in custody.
Fire crews from Worthing and Lancing were called to the scene after the fire broke out in a ground floor bedroom.
Firefighters wearing breathing equipment were able to use a high-pressure hose to bring the fire under control and the all clear was given at 10.30pm.
West Sussex Fire and Rescue Service (WSFRS) said the fire caused smoke damage to the building and serious damage to the room where the fire began.
A fire service spokesman said the fire was started deliberately.
Video by Eddie Mitchell.