Kiessling will miss Leverkusen's last two league games of the season with the Werkself holding onto fourth in the league, which carries a Champions League play-off berth, by just a point from VfL Wolfsburg.
Bayer crashed out of this season's Champions League with a 6-1 aggregate defeat at the hands of Paris St Germain in the last 16 and fired coach Sami Hyypia earlier this month after a run of defeats in a bid to protect their status in next season's competition.
The loss of Kiessling is a blow to their hopes under caretaker coach Sascha Lewandowski with a fortnight left in the season.
The 30-year-old suffered the injury in Leverkusen's 2-2 draw at home to second-placed Borussia Dortmund on Saturday and a scan confirmed the worst, meaning he will miss his side's final two matches, at home to Eintracht Frankfurt and away to Werder Bremen.
Having made his last international appearance at the 2010 FIFA World Cup™, Kiessling was the Bundesliga's top-scorer last season with 25 goals in 34 league games and has hit the net 19 times for Bayer this season.