A number of other people were also held as police raided nine offices and homes in north-eastern Catalonia.
The arrests are part of an investigation into rights sales relating to Brazil, police sources say.
Rosell was Barca president from 2010 to 2014, when he resigned following a Spanish court's decision to investigate the 2013 signing of Brazilian Neymar.
In June 2016, Barcelona paid a fine of 5.5m euros (£4.7m) over the 25-year-old's move from Santos. The club was accused of tax fraud, which it denied.
Rosell's wife was among those also arrested on Tuesday.
Spanish newspaper El Confidencial reports the arrests are part of a joint operation between the Spanish police and the FBI, related to the United States-led investigation into corruption at Fifa.
The investigations into alleged corruption at football's governing body began two years ago, and Swiss authorities raided a Zurich hotel where Fifa delegates were staying for their annual conference.
Seven people were arrested in the raid, which was carried out on behalf of the United States Department of Justice.
More arrests and indictments on corruption charges followed in subsequent days and scores of Fifa officials and associates have since been arrested in connection with the investigation.
In March, Fifa passed on evidence from its internal inquiry to Swiss and US authorities.

The blaze at The Swan in Waters Upton, on the outskirts of Telford, started at about 00:50 BST and was brought under control within four hours.
The roof was "very badly damaged" and slates were lying shattered on the pavement outside the pub, BBC Radio Shropshire reporter Ian Perry said.
The cause of the fire at the property, which closed in 2007, is not known. An investigation is under way.
About 40 firefighters from from seven stations - Bridgnorth, Hodnet, Shrewsbury, Telford, Telford Central, Tweedale and Wellington - were deployed.
Former Barcelona president Sandro Rosell has been arrested as part of a money-laundering investigation.
[NEXT_CONCEPT]
A fire broke out at a disused pub in Shropshire in the early hours.