Di Maria scored the opening goal in Monday's 3-0 win over Sassuolo in his first game for his new club after his move from Paris Saint-Germain.
The 34-year-old also set up Dusan Vlahovic for the second of his two goals but was substituted midway through the second half.
Juventus said scans showed Di Maria had suffered a "low-grade lesion" to his left thigh, adding that the injury would be re-evaluated in 10 days.
He will miss at least the next two league games against Sampdoria and Roma.
Juventus were already without Paul Pogba, who hurt his knee on a pre-season trip to the US after rejoining the Turin club following six years with Manchester United.
The France midfielder is undergoing a course of "conservative therapy" and could return in mid-September.
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