The England forward was forced from the field after 66 minutes of the 3-2 win over title rivals Manchester City on Sunday with what appeared to be a hamstring problem.
"He may struggle for the weekend but it's not too serious," said manager Brendan Rodgers.
"It's not too serious and won't keep him out for too many weeks, but he may be out for the weekend.
"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 [against Stoke].
"It's certainly not as serious as what sometimes a hamstring injury can be."
Sturridge took to Twitter to express his frustration at being sidelined.
The 24-year-old former Chelsea and Manchester City forward has scored 20 goals this season and formed a lethal partnership with Uruguay striker Luis Suarez to leave Liverpool close to their first league title since 1990.
Liverpool top the table with 77 points from 34 matches, two clear of Chelsea with City on 71 after their 2-2 draw with Sunderland on Wednesday but with a game in hand.
After the trip to relegation threatened Norwich, Liverpool host title rivals Chelsea then face Crystal Palace away before ending their campaign at home to out of form Newcastle United.
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