Leicester City will be without Jamie Vardy for Sunday's clash with Arsenal.
The 35-year-old only recently returned from a hamstring problem which kept him out for two months.
"Vards will be out," Rodgers said on Wednesday.
"He unfortunately got injured in the last game so is going to be out for a few weeks, which is a shame.
"He just got a knock towards his knee, but hopefully in the next three to four weeks, he responds okay.
"He felt a soreness on it after the game the other day. It's very frustrating for both [the club and the player].
"For him in particular, having been out, working so hard to get back, you can see the difference he makes to the team.
"Of course, for us as coaches and managers and players, it's frustrating because you miss that level of player.
"Hopefully he can get back, get fit again, and we'll see how is in a few weeks."
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