The France star was hurt during the first half of Wednesday's 3-1 win at Montpellier in Ligue 1 having earlier had two penalties saved.
PSG coach Christophe Galtier had initially suggested Mbappe had suffered a knock to the back of the knee rather than a muscle injury, but tests have since confirmed the true extent of the problem.
"After undergoing tests, Kylian Mbappe suffered an injury to the left thigh at the level of the femoral biceps," said a club statement.
If he misses three weeks as expected, Mbappe can also expect to sit out next midweek's French Cup last-16 tie against Marseille and faces a race against time to return for a potentially pivotal Ligue 1 game away to the same opponents at the end of this month.
However, PSG will hope that Mbappe, who has scored 25 goals in 26 appearances for his club this season, will be fit for the second leg against Bayern in Germany on March 8.
The news is a bitter blow for the French giants, who are desperate to avoid a repeat of what happened last season when they were knocked out of the Champions League in the last 16 by Real Madrid.