Doctors confirmed Di Maria will miss the semi-final against the Netherlands because of a thigh problem but did not rule the winger out of being fit for the final should Argentina prevail in Sao Paulo on Wednesday.
"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," team doctor Daniel Martinez told reporters.
Brazil captain Thiago Silva was also expected to miss the semi-finals after picking up his second yellow card of the tournament in the 2-1 win over Colombia in the last eight on Friday.
The central defender was cautioned for needlessly blocking keeper David Ospina as he was taking a kick and Fifa said they were analysing an appeal from the Brazilian Football Association.
His presence in the team on Tuesday would be a huge fillip for a Brazilian public still reeling from the loss of talismanic striker Neymar, who was ruled out of the rest of the tournament after fracturing a vertebra in the win over Colombia.
That incident continued to appear on Sunday's sports news bulletins on local television but Brazil's former World Cup winning captain Carlos Alberto Torres hoped it might end up being a good omen for the current squad.
The 1970 skipper recalled how Amarildo and Garrincha had stepped up to fill the void left by an injury to Pele in 1962 and helped steer Brazil to the title.
"In the 1962 World Cup, we lost Pele," he told Sportv. "Maybe someone will wake up and become the Garrincha of 1962."
Germany were sure Neymar's absence would not weaken the challenge facing them in Belo Horizonte, with Bastian Schweinsteiger expecting Brazil to draw strength from the adversity suffered by their poster-boy.
Schweinsteiger's coach Joachim Loew, however, was more concerned about the methods Brazil might use in the mouth-watering last four clash, wary of a repeat of the tough tackling that marked their win over Colombia.
"There's precious little left of that traditional Brazilian style of soccer, that artistic style of playing that we all know so well," Loew said in an interview at his team's base camp on the Atlantic coast.