Bent suffered the setback during the Barclays Premier League match at Wigan nine days ago.
The former Tottenham and Sunderland player will be able to resume training in around three months - just as England start their campaign in Poland and Ukraine.
A Villa statement read: "Darren Bent underwent surgery tonight in a London clinic to repair ruptured ligaments in his left ankle.
"The operation was a complete success and it is expected that Darren will be able to resume full training in around 12 weeks."
Club record signing Bent is Villa's leading scorer with 10 goals during the campaign.
He had been hoping to play in his first major tournament with England after missing out on selection for the 2006 and 2010 World Cups.
But now Bent will channel all his energies into ensuring he is fully up to speed for the 2012-2013 campaign - and potentially a role at the Olympics.
Bent was one of three over-age Villa players asked if they would be available for Team GB and will be eligible as he is not taking part in Euro 2012.
Source: PA
Source: PA