Aguero looked comfortable in training at the Argentine camp, but Di Maria was missing and undergoing intensive treatment after hobbling out of their 1-0 quarter-final win over Belgium.
In their first semi-final since 1990, the South Americans play the Netherlands 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.
"Sergio has practiced three times. He's ready to play."
Aguero missed two games due to a muscle strain but on the evidence of Sunday's afternoon training session at their camp in Belo Horizonte, the speedy forward should at least make the substitutes bench.
Higuain's instinctive strike against Belgium gave Argentina passage to the semi-finals.
Roared on by tens of thousands of fans who have crossed the border, Argentina are bidding for a third World Cup. To achieve it on the soil of rivals Brazil would be especially sweet.
The squad looked relaxed during training, laughing and joking with coach Alejandro Sabella.
They are based at local team Atletico Mineiro's training complex, where motivational banners in blue-and-white colours give them encouragement as fans huddle at the gates outside.
"The group as a whole is very happy, except for the situation with Angel, which is a great shame," midfielder Javier Mascherano told reporters. "We hope he recovers soon."
Mascherano said Argentina's improved performance against Belgium was due to a more intelligent approach, which they had to repeat against the skilful Dutch.
"Against Belgium, we used the spaces better. We didn't rush. We waited for the right moment to pass," he said.
"It was a lovely game but it was yesterday. Now we're focused on Holland. We know they are still smarting from defeat (in the final) in South Africa four years ago.
"We've come far, Argentines have waited 24 years for this, but we want to go further."
Defender Jose Basanta said he had been dreaming all his career of playing in the World Cup.
"I'm so happy. Argentina are making history, but we've not won anything yet," he added.
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