In a statement, Juve said Di Maria underwent tests on Thursday "which revealed a low-grade lesion to the hamstring of the right thigh".
"It will take around 20 days for the player's complete recovery," Juve added.
Argentina winger Di Maria was substituted 23 minutes into Juve's shock 2-0 defeat which left them on the brink of elimination from the Champions League.
Juve are third in Group H and five points behind second-placed Benfica with two matches remaining following a loss which led to both coach Massimiliano Allegri and president Andrea Agnelli to say they were ashamed of the team.
It is the latest absence for the 34-year-old, who was set to return to Serie A action following a two-match suspension and had already been injured twice since arriving as a free agent in the summer.
He will miss both Juve's final group fixtures at Benfica and with leaders Paris Saint-Germain.
Juve, who are also 10 points behind Serie A leaders Napoli, travel to local rivals Torino on Saturday.