The former Benfica ace impressed in the first half of Madrid's victory as he created three goals, but was forced to leave the pitch in the 49th minute after picking up a knock.
Di Maria will undergo further examination on Monday to clarify the exact extent of the problem, but Mourinho fears he will have to make do without the winger for a while.
"He has a hamstring injury. We will have to wait for results of further tests, but I have enough experience to realise that he will be unavailable for some time," the Portuguese coach said during the post-match press conference.
Di Maria has withdrawn from the Argentina squad for the upcoming 2014 World Cup qualifiers at home versus Bolivia on November 11 and away against Colombia four days later due to the injury.
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