McArthur, who tweeted that he could miss the rest of the season, picked up an ankle injury during Palace's 2-1 defeat to Bournemouth on Tuesday, while Puncheon is struggling with a hamstring problem.
"I have some disappointing news: McArthur and Puncheon are out for a long period," Pardew announced at a news conference ahead of Saturday's clash with Swansea City.
"[Dwight] Gayle and [Sullay] Kaikai have trained and are available. I would have probably used Sullay in this period without [Yannick] Bolasie, had he been fit.
"[Yohan] Cabaye should be back for Saturday. [Bakary] Sako and Bolasie for Spurs [in the FA Cup on February 20].
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"Puncheon and McArthur have both been having fabulous seasons for us, so that's a significant blow."
Emmanuel Adebayor came off the bench to make his Palace debut against Bournemouth and Pardew hit out at some of the striker's critics.
"I thought some of the reporting the other night was very critical of Ade," he added. "He doesn't sprint around like a [Jamie] Vardy, but he was sharp. He's a bit different to a Palace player.
"Ade's almost ready for a start. He'll have a cameo role on>