Kiessling suffered the injury in the closing stages of Leverkusen's 2-2 draw with Borussia Dortmund on Saturday, and will play no further part in the season for Sascha Lewandowski's men.
The 30-year-old has scored 15 goals in the Bundesliga this season to help Leverkusen into the top four, including five in his last eight appearances.
However, he will not be able to add to that tally, leaving Lewandowski with a gap to fill as Leverkusen look to hold off Wolfsburg and seal UEFA Champions League football.
A club statement confirmed: "An MRI scan on Sunday morning confirmed the 30-year-old suffered a torn muscle in his left thigh in the closing stages of the match against Borussia Dortmund.
"Kies will be sidelined for the last two games of the season away to Eintracht Frankfurt and at home to Werder Bremen."
