"It is a sign of the continued interest of the Berlusconi family who have always been close to the club and offered economic support," Milan chief executive Adriano Galliani told reporters.
"The fact that the club president's brother (Paolo) and one of his daughters are on the board is a good sign which must also be welcomed by fans as an act of faith."
Fans had criticised Italian prime minister Berlusconi for a lack of investment following the sale of Kaka to Real Madrid in 2009 but they have been silenced by a mini spending splurge at the start of the season and the club closing in on the title.
Media reports have long linked Milan with a possible bid by Arab investors but Berlusconi has denied any immediate interest in selling.
Barbara, 26, has been touring departments of the club for the last year to get used to the organisation and has been the subject of vast Italian press coverage speculating about her relationship with Milan's Brazil striker Alexandre Pato.
The Italian football federation also said in a statement on Wednesday that Milan forward Zlatan Ibrahimovic's appeal against his three-game Serie A ban for swearing at a linesman had been rejected.
