Looney is slated to undergo an MRI on Tuesday, but "there isn't great optimism on a return," in the Finals, per ESPN's Adrian Wojnarowski.
The fourth-year center exited the game in the first quarter on Sunday night after colliding with Kawhi Leonard.
Looney joined the Warriors in 2015 after being selected with the No. 30 overall pick. He is averaging 7.2 points and 4.6 rebounds per game this postseason.
Klay Thompson led Golden State with 25 points in Sunday's 109-104 win. Thompson injured his hamstring in the fourth quarter, and is questionable for Game 3.
Tip-off from Oracle Arena in Oakland on Wednesday is slated for 9 p.m. ET.