The 29-year-old was forced off after just 18 minutes of his side's EFL Cup match against Southampton on Wednesday night, watching on as the Eagles fell to a 2-0 defeat.
"Scott Dann has a slight strain in his hamstring, definitely will miss this game and possibly Everton as well. Tomkins is fit. That's why we invested heavily in him, so we could seamlessly fit him in to that centre-half position, so that's worked out okay for us," he told the club's official website.
"I rested some players [against Southampton] due to the Premier League demands and with our squad we needed to make sure we got everybody up to speed. Although the result didn't go well for us, those guys will be better for it."
Palace currently sit eighth in the Premier League table after five games.