The Brazilian scored the opener in PSG's routine 3-0 semi-final victory on Wednesday but was forced from the pitch with around 20 minutes remaining.
Medical update: Marquinhoshttps://t.co/VNhD1MQUNC— Paris Saint-Germain (@PSG_English) January 24, 2020
He looks set to miss Ligue 1 games against Lille, Montpellier, Nantes and Lyon, plus next week's Coupe de France date with third-tier Pau.
In a statement, PSG announced: "Marquinhos suffered a hamstring injury on Wednesday at the Stade Auguste Delaune, and examinations confirmed a lesion of the biceps femoris.
"He is expected to be unavailable for three weeks."
PSG will hope to have the 25-year-old fully fit for the first leg of their Champions League last-16 tie against Borussia Dortmund on February 18.