Sturridge was substituted off in the 3-2 win over Manchester City on Monday, and although Rodgers has said that it is only a minor injury he does not expect him to be fit for the Norwich clash.
"It's not too serious and won't keep him out for too many weeks, but he may be out for the weekend," Rodgers told the club's official website. "We'll assess it more over the next couple of days, but that's how we're looking at it at the moment.
"He may well make a real good recovery over the next few days and be ready for the weekend. At this moment in time we're just assessing him and seeing how he goes because he does recover very quickly.
"Before the first game of the season, he'd only played 45 minutes of football before he played and scored the winner. It's certainly not as serious as what sometimes a hamstring injury can be."
Liverpool are currently top of the league by two points with four games left to play.