Cousins will likely miss the remainder of the postseason but is not expected to require surgery, according to The Athletic's Shams Charania.
Doctors are working toward determining the severity of the injury, which will allow them to better evaluate the recovery time, sources told ESPN's Adrian Wojnarowski.
The 28-year-old sustained the injury in the first quarter of Monday's 135-131 Game 2 loss to the Los Angeles Clippers. He limped to the locker room and did not return.
Cousins suffered an Achilles tear in January 2018 while with the New Orleans Pelicans. He returned to action this past January after signing a one-year deal with the Warriors and appeared in 30 regular-season games.
The four-time All-Star will once again hit free agency in July but may struggle to find suitors depending on the severity of the injury.
Cousins averaged 16.3 points and 8.2 rebounds in 25.7 minutes per game.