Sky News, citing reports in the Spanish media, said the building concerned is a restaurant, which has been named by local media in Palma as the Medusa Beach Club.
The incident happened at around 8.30pm local time (7.30pm BST) in Carrer de Cartago (Cartago Street). The BBC reports several people were believed still to be trapped in the building following the collapse.
Balearic emergency services confirmed shortly before midnight local time (11pm BST) four people had been killed and 16 injured, nine very seriously and seven seriously. The injured have all now been taken to hospital.