The fire department tweeted that the bus had 11 people on board when it ran off the road near the popular Marina Grande area of the island.
Local media reports have identified the victim as Emanuele Melillo, 33, who leaves behind a pregnant wife.
More than a dozen others were injured in the incident, with several people believed to be in a serious condition.
Six passengers were hospitalised, including a 15-year-old boy, according to Italian news agency ANSA.
The minibus was reportedly “more crowded than usual”, due to a breakdown on the island’s funicular railway line on Thursday morning.
The vehicle overturned and remained wedged between a wall and cabins at the Marina Grande beach, according to reports.
Emergency services rushed to the scene, with an air ambulance sent from Naples.
Capri’s mayor said the cause of the crash was not immediately clear, Italian daily La Repubblica reported.
