Slimani suffered a groin injury, while midfielder Nampalys Mendy was ruled out for the rest of the season after undergoing ankle surgery.
"Unfortunately Wes Morgan won't make it (for Wednesday's game with Arsenal)," Shakespeare told a news conference on Monday. "The first impression was it was cramp but I think he just overstretched his hamstring.
"We're hoping the caution on Wednesday will mean we can look to Saturday (against West Brom)."
Leicester, currently 15th in the league, have picked up five victories in their last seven league games to move six points clear of the relegation zone.
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Shakespeare, however, is not sure about the points tally needed to survive the drop and has urged his side to keep fighting for results in the final six games of the campaign.
"I'm not sure how many points survival will take. All teams are capable of wind," he added.
"We aren't safe. Even if we get there we've to keep trying to win. Competitiveness is vital in football. We need it to the end."
Following the trip to the Emirates, Leicester travel to the Hawthorns to face eighth-placed West Bromwich Albion on Saturday.
(Reporting by Hardik Vyas in Bengaluru; Editing by Gareth Jones)
