The women state in a police report that they were subjected to sexual assault and forced to work under slave-like conditions in Julio Iglesias' homes in the Dominican Republic and the Bahamas.
The artist is said to have sexually assaulted the women, monitored their mobile phones and forced them to work up to 16 hours a day, according to the television company Univision and the newspaper El Diario.
The Spanish Minister of Equality, Ana Redondo, has called for the allegations to be investigated.
Julio Iglesias, 82, is one of the Spanish-speaking world's biggest artists and also had great success with English-language albums in the 1970s and 1980s. He has not yet commented on the allegations.
