The detentions were part of a money-laundering investigation related to buying television rights for past matches of Brazil’s national team.
Three other people were detained, but their identities were not immediately released by authorities.
Police raided offices, homes and businesses in Barcelona and other locations in Spain as part of “Operation Rimet”, a reference to former Fifa president Jules Rimet, who also gave his name to the World Cup trophy from 1930 to 1970.
Authorities said the operation looked into the alleged illegal payments received by Rosell and other people involved in promoting Brazil’s games. Authorities said nearly €15 million (£13m) could have been laundered through tax havens.
Officials said the operation used information from the FBI following the US case against high-level Fifa officials in 2015.
Rosell, a former Nike executive in Brazil, had close connections to the former president of the Brazilian football confederation, Ricardo Teixeira, who was mentioned in the indictment by American officials.
Teixeira was being investigated by Spanish authorities, and raids were also expected in Brazil. Teixeira resigned from the Brazilian confederation in 2012 citing medical reasons amid widespread allegations of corruption and irregularities in his administration.
In the 1990s, Rosell negotiated several deals with Teixeira involving Brazil’s national team and Nike, which remains the sportswear company used by the Brazilian team.
Several years ago, Rosell was formally accused by Brazilian authorities of using one of his companies to benefit illegally from a friendly between Brazil and Portugal in 2008. Rosell was cleared of any wrongdoing at the time.
In a separate case in Spain, Rosell is going to stand trial for fraud and corruption charges involving the transfer of striker Neymar from Brazilian club Santos in 2013.
Prosecutors said the real amount of the transfer fee was concealed to benefit some of those involved.
Neymar and his father will also stand trial.
Rosell resigned as Barcelona president in 2014 because of the allegations related to Neymar’s transfer.
He had taken over the club in 2010. He and his wife were detained at their home in Barcelona during one of the police raids.