Ladislav Rehák is chairman of the board of Orange, the country's largest mobile operator, and owns or manages 17 other companies, including several media such as the Týždeň weekly.
Police have slapped an "information embargo" on the case, but police corps president Ján Packa said the three Reháks had been charged with extorting money from a female accountant who worked for them for two years.
Packa said the men had forced the accountant to sign a statement at a public notary acknowledging that she owed them Sk5 million.
However, the men, through their lawyer Ondrej Mularčík, said that the accountant had actually embezzled the sum from their firms, and that rather than going to the police they had chosen to get her to acknowledge the debt and repay it.
The police say a doctor confirmed that the accountant was "slightly injured", and that this medical report forms part of the evidence against the men, whose crime is considered exceptionally serious under Slovak law.
Mularčík said there was nothing to confirm that any one of the Reháks had caused the woman's injuries. He also objected to the reasons the prosecution cited in requesting pre-trial custody, saying that Rehák was unlikely to flee trial, as the prosecution claimed, given that he had returned home from a trip to the Czech Republic immediately when he heard that his sons had been arrested.
Packa claimed the entrepreneur and his sons had been arrested because police wanted to prevent them from carrying out their aims.
Police dubbed their planned raid Svätuškár (Holy Roller), although Packa denied that the choice of name had anything to do with the fact that Rehák had sponsored the opposition Christian Democrats with a gift of Sk600,000 in 2003.
According to Packa, the name of the raid was taken from the day it began - All Saints Day, November 1.