The move comes a week after United activated a similar extension to Marouane Fellaini's contract.
Ecuador international Valencia, 31, was bought as a winger from Wigan in 2009 for an undisclosed fee.
He was converted into a full-back by former United boss Louis van Gaal, having been used occasionally in the role by Sir Alex Ferguson.
Valencia has made 23 starts for United this season, a total exceeded only by Paul Pogba and Zlatan Ibrahimovic among the outfield players in Jose Mourinho's squad.
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Manchester United have triggered a one-year extension to Antonio Valencia's contract, signing him up until 2018.