The Real Madrid winger lasted just 33 minutes of the quarter-final in Brasilia before limping out of the action.
His agent Eugenio Lopez, who works alongside Jorge Mendes, revealed to Goal Argentina that the 26-year-old had told him he had a torn thigh muscle, ruling him out of the rest of the tournament.
Argentina are due to face the winner of the Netherlands/Costa Rica tie in Sao Paulo on Wednesday with the final due to take place in Rio next Sunday.
Further tests will be carried out tomorrow after which it is expected the news will be confirmed by team doctors.
His absence would be a huge blow for a side already over-reliant on Lionel Messi.
Di Maria has played well in bursts in Brazil but has yet to replicate the form which helped Madrid to the Champions League crown in May.
One consolation for coach Alejandro Sabella is the fact that one of his other star forwards, Gonzalo Higuain, stepped up against the Belgians, grabbing the first-half winner with a clinical shot on the turn.
After the game Sabella admitted he had his fingers crossed that Di Maria would be fit enough to play a part in the tournament going forward.
“Di Maria's injury could be costly for us. Angel has a problem with his thigh and will undergo tests tomorrow," he explained.