"It was a bad injury but with the level of treatment he has had and the post-operative prognosis we've been given, we're all hoping to see him back, perhaps sooner than everyone expected on Saturday night."
The injury happened in the first 15 minutes of the match against Danish side Odense at Villa Park.
Bouma's team-mates looked on in shock as the left-back underwent treatment before being replaced by Gareth Barry.
The Dutchman was taken to hospital where an X-ray showed his right ankle was dislocated rather than broken - and Villa boss O'Neill initially feared the worst.
"I am a bit squeamish and the pictures were not so good," said O'Neill after Villa's 1-0 win, which gave the Midlands club a 3-2 aggregate victory and a place in the final qualifying round of the Uefa Cup.
Bouma joined Villa from PSV Eindhoven for £3.5m in August 2005 and O'Neill added: "It's terrible news because he played every single game last season. He was fantastic but he'll come through it."
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