The 29-year-old forward was sent off for a horrific tackle on Nicolas Tagliafico in a dramatic 3-3 draw with Ajax last month, Bayern’s final game of Group E.
Muller made contact with Tagliafico’s head while challenging for the ball and the match had to be paused as the Ajax defender received medical treatment on the ground.
The Germany international apologised to Tagliafico following the incident and has now been handed his punishment by UEFA.
Liverpool host Bayern at Anfield in the first leg of the Champions League clash on February 19 before heading to the Allianz Arena for the return leg on March 13.
Speaking after his red card, Muller said: ‘I would like to apologise to Nico Tagliafico.
‘There was no intention [in the foul] . Get well.’