Rojo was due to fly out to the States on Saturday but passport issues meant he stayed at home.
Louis van Gaal was said to be far from pleased with the Argentine for not renewing his passport despite having an extended break following the Copa America.
The defender is set to be fined two weeks wages, or £140,000, for the error.
Angel di Maria also missed the flight as he closes in on a £45m move to Paris Saint-Germain.
Victor Valdes and Robin van Persie have been on the wrong end of van Gaal’s ruthless streak in recent weeks and Rojo’s error would have infuriated the Dutchman.
It is unclear whether or not Rojo will be able to make it to America in time for United’s final game of the tour against PSG. If he doesn’t, it is highly likely that he will miss the opening game of the Premier League season against Tottenham Hotspur.