Jones hobbled off in the second half of England's 2-0 win in Switzerland on Monday and he is now likely to be unavailable for a number of weeks.
"Phil has a torn hamstring," Van Gaal said.
"He is maybe out for three weeks or a month."
If Jones is out for a month he will miss United's next four games and his place in the England squad for October's double-header against San Marino and Estonia would also be in doubt.
It is an injury blow that the winless United boss could do without, particularly when his team have looked so vulnerable defensively in their opening three league matches.
Van Gaal, speaking at a press conference at the Aon Training Complex in Carrington, said nine of his players are unavailable for Sunday's game against QPR through injury.
Source : PA
Source: PA