Members of a Colombian family employed by the Paris Saint‑Germain defender claim they were made to work long hours without holidays and without the legal documents required for their employment.
Their lawyer, Lola Dubois, said the family suffered economic vulnerability and claimed they experienced a form of "modern slavery".
She said work contracts were drawn up a year after they started their roles.
The 29-year-old Hernandez, who won the 2018 World Cup, and his wife Victoria Triay said they had been manipulated and had their trust betrayed by the father, mother and their three children.
"These people shared our life with us with respect and dignity," Hernandez and his wife said in a statement.
"This matter is now being handled through the appropriate legal channels."