The Manchester United winger dislocated and fractured his left ankle in a horrific moment in Tuesday's goalless draw with Rangers.
But the club are confident he will return after admitting he is likely to miss the rest of the season.
Big worries: Wayne Rooney looks on as Antonio Valencia is treated on Tuesday night
A United spokesperson said: 'The operation went well. A plate has been inserted to stabilise the fracture but there is obvious significant ligament damage that follows a dislocation and he will be out for a good portion of the season.
'Contrary to recent reports there has been no official contact from the Ecuadorian national team. Antonio is perfectly fine, very positive and very determined.'
Sportsmail revealed how Sir Alex Ferguson was at Valencia's hospital bedside by 9am on Wednesday to reassure the winger that he still has a future in football.
Nightmare: Valencia suffered the double break after catching his studs in the turf
Although the Ecuador international faces a struggle to play again this season, Ferguson told him he will make a recovery.
A friend of Valencia told Sportsmail: 'Antonio is devastated and finding it hard to come to terms with what has happened. But it cheered him up that Sir Alex came in to see him. He really appreciated that.'
In the immediate aftermath of the incident, Ferguson ruled Valencia out of the remainder of the campaign and likened the injury to one suffered by Alan Smith in 2006.
When Smith suffered his injury in a freak incident against Liverpool at Anfield, he was ruled out for seven months, claiming afterwards that his eventual return came too soon.
Horror: Kirk Broadfoot can't bear to look after the incident at Old Trafford
A similar timescale would have Valencia back in action by April, although by that stage Ferguson might not want to be pushing the winger anyway.
After an impressive first season at Old Trafford, Valencia had been hoping to make further improvement.
Instead, he must battle to recover from such an awful setback, with Darren Fletcher among those who feel he will be back.
He said: 'He is a strong character and a good lad. He has real determination and works hard. He will be back I am sure. He will have a long future at Manchester United.'
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