The 31-year-old has played an important role for Jose Mourinho's side this season, making 11 appearances in all competitions.
However, Valencia was absent from United's squad facing Burnley on Saturday after the club confirmed the right-back has fractured an arm.
The official club Twitter feed posted: "Antonio Valencia has a fracture in his arm and will have surgery today".
Matteo Darmian is starting on Saturday in place of the Ecuador international, who joins fellow defenders Eric Bailly and Chris Smalling on the sidelines through injury.
"They were the three players that start almost every match in the Premier League and now we lose all three in the same period," manager Jose Mourinho told broadcasters.
"But that's football and it's an opportunity for others to play
We trust Darmian and we trust Marcos Rojo to have a positive influence."
Attacking midfielder Henrikh Mkhitaryan was among the other notable absentees from the United squad on Saturday.
Much was expected of the 27-year-old following his summer arrival from Borussia Dortmund, yet his playing time has been restricted.
While a thigh injury played a part, Mkhitaryan's return to fitness has not brought with it a recall to the squad and that absence continued when Burnley arrived on Saturday.
Mourinho said on the eve of the match that the player was taking time to get used to Premier League life, but Football Federation of Armenia president Ruben Hayrapetyan has suggested the player is puzzled by his exclusion.
"I cannot know what the Manchester United manager is thinking about," Hayrapetyan said, according to Armenpress.
"I have talked with Mkhitaryan
He also doesn't know what Jose Mourinho is thinking.
"Mkhitaryan trains and is in good shape, but no-one knows the reasons."
Source : PA
Source: PA