Winger Di Maria hobbled out of Argentina's quarter-final clash against Belgium on Saturday, the former double World Cup winners coming out on top 1-0 after Gonzalo Higuain's fine early strike.
It has been confirmed that Di Maria will now miss Argentina's semi-final against the Netherlands on Wednesday 9 July in Sao Paulo, as a result of a 'Grade A' thigh strain injury.
Argentina's team doctor, Daniel Martinez, told reporters: "Angel has a Grade 1 injury. Of course he won't play in Argentina's next game. After that, we'll evaluate the situation day-by-day."
The Real Madrid player had helped his side beat Switzerland 1-0 in the second round of the tournament with a 118th-minute goal in extra time, although he could still play in the final on Sunday should Argentina make it that far.
While the 26-year-old will be missing in action against Holland, the good news for Argentina is that Aguero will be fit to face the Dutch after recovering from a hamstring injury picked up during the side's group-stage victory over Nigeria.
"Sergio has practiced three times. He's ready to play", Martinez added.
Manchester City striker Aguero has not yet scored during the 2014 World Cup, and is 15/2 with Betfair to score first in Wednesday's semi-final.
Enzo Perez is expected to take over Di Maria's position on the pitch, while a groin injury may continue to keep Nigel De Jong out of the World Cup semi-final for the Dutch.
Argentina's star performer Lionel Messi will look to score at least two goals in the remainder of the World Cup to draw level with Colombia's James Rodriguez for Golden Boot honours, and is 4/1 with William Hill to score first against the Netherlands.
Holland and Argentina's semi-final match gets underway this Wednesday at 9pm in Sao Paulo, which will be shown live on ITV. You can compare all the odds for the 2014 World Cup right here.
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