The 30-year-old posted a picture on social media from his hospital bed to say the surgery had gone well and he will now begin a rehabilitation process.
Valencia was kicked on the foot during the first half of United's goalless draw against Manchester City on October 25 but played on until late in the game before being replaced by Matteo Darmian.
The Ecuador international had just ousted summer arrival Darmian as Louis van Gaal's first-choice right-back but now faces an unspecified time on the sidelines having gone under the knife.
"#mufc can confirm @Anto_V25 has had an operation on his foot," the club posted on their official Twitter feed.
Valencia then followed up with a picture of himself just after the procedure.
"Thank God came out well from the operation
Now think about my recovery," he wrote.
In Valencia's absence, both Darmian and Ashley Young have started two games apiece at right-back as Van Gaal's Red Devils continue to boast the best defensive record in the Barclays Premier League.
Saturday's 2-0 win over West Brom was enough to see United close to within two points of the top of the table heading into the international break.
Valencia joins fellow full-back Luke Shaw on the injured list, with the England international sidelined for the coming months after suffering a double leg-break during United's 2-1 Champions League defeat at PSV Eindhoven in September.
Source : PA
Source: PA