The midfielder sustained the problem while sprinting forward for an effort on goal against the Eagles, before immediately signalling to the bench for a substitution.
The injury comes at the worst possible time, with Oxlade-Chamberlain now set for a lengthy spell on the sidelines as he enters the final year of his Liverpool contract.
Having struggled for opportunities towards the end of the previous campaign, the 28-year-old will now be playing catch up with the rest of his teammates for the majority of the first half of the season.
After Klopp told reporters the injury was a serious one earlier this week, a possible timescale for Oxlade-Chamberlains absence has now been revealed.
Writing in the Athletic, James Pearce claims Oxlade-Chamberlain is unlikely to play again before October. That would mean the former Arsenal man would be sidelined for between two and three months.
Pearce also adds that the injury is not expected to see Liverpool move for another midfielder this summer, with Klopp still happy with his options in the centre of the park.
This certainly looks like the beginning of the end of Oxlade-Chamberlains time at Anfield, with a new contract surely unlikely at this stage.
The injury should also rule out any outside chance of him making the England squad for the World Cup, with his last cap coming in November 2019.
Meanwhile, another Liverpool player currently sidelined is goalkeeper Caoimhin Kelleher, who picked up a groin injury on international duty at the end of last season.
Klopp told reporters on Thursday that the Irishman is expected to be out for another two or three weeks, with Pearce claiming Kelleher is likely to return in mid to late August.