The Algerian sustained the injury in a collision with West Brom goalkeeper Boaz Myhill during Saturday's 2-0 Premier League defeat.
Palace physiotherapist Alex Manos confirmed to the club's official website that the 27-year-old faces a lengthy spell on the sidelines.
"The challenge itself was pretty innocuous," he said. "But it was knee against ribs and when that happens, there was only ever going to be one winner.
"Adlene is looking at upwards of six weeks out now.
"It will take four to six weeks for the injury to heal and then another couple to get back into full training."
Palace are currently bottom of the Premier League with a solitary victory to their name.
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