Red Devils medical staff have assessed the Ecuador winger on Thursday morning and confirmed Valencia has also suffered ligament damage.
"The operation went well, a plate has been inserted to stabilise the fracture but there is obviously significant ligament damage that follows a dislocation," read a statement from United.
"He will be out for a good portion of the season."
The statement also denied claims attributed to the Ecuador team doctor about Valencia's mental state and insisted the former Wigan star was feeling positive about his recovery.
"Contrary to recent reports, there has been no official contact from the Ecuadorian national team," read the statement.
"Antonio is perfectly fine, very positive and very determined."