The pop singer was speaking during a weekend benefit for the HIV support organization Body and Soul in London, Sky News said.
"This charity is really important to me because one of my family is HIV positive. And I am so, so proud of him," she said during the concert.
The TV personality and other members of the Osbourne family had been introducing a performance by the Scissor Sisters at the time.
Photographers at the concert reported that she started sobbing before leaving the stage, Sky News said.
The singer rose to fame on the reality TV show "The Osbournes," which followed the antics of her father and his dysfunctional family.