Antonio Valencia was substituted after seven minutes of Manchester United's pre-season friendly against San Jose Earthquakes with a suspected calf injury.
Valencia, who was appointed as United's club captain, was replaced by Matteo Darmian in Sunday's friendly at the Levi's Stadium.
United are yet to disclose the extent of Valencia's injury.
Jose Mourinho confirmed on Thursday new signing Diogo Dalot, also a right-back, will be out until September with a knee injury.
That leaves Darmian as the only fit senior right-back in Mourinho's squad ahead of the new Premier League season.
The Italy international, however, is the subject of interest from Napoli, whose president Aurelio De Laurentiis confirmed they are "monitoring" the 28-year-old as they attempt to sign a versatile full-back.
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