The 33-year-old, who is out of contract at Villa this summer, has been sidelined all campaign by groin and hip problems.
It has been an injury-plagued 12 months for the Republic of Ireland international who was also out for nearly three months with a shoulder problem before returning at the very end of last season.
Dunne's last game was the Republic of Ireland's 2012 European Championship group stage defeat by Italy.
Along with Ron Vlaar - who is also sidelined through injury - Dunne has been a big loss for Villa, who have conceded the joint most goals in the Premier League this season and currently occupy 18th place in the division.
Villa boss Paul Lambert said: "If you look when Richard did his shoulder, he only came back for a couple of games and then had the groin problem at the Euros.
"He's not played much football for a year really. But the (latest) operation in America was successful and the main thing for everyone is to get him back fit."