The 2013 winners, 2010 and 2012 finalists and last year's semi-finalists will be looking to continue a proud record on the continent by crossing the next hurdle which lies between them and a place in Berlin in June.
bundesliga.com brings you all you need to know about the record champions' trip to Ukraine...
Five-time European Champions Bayern are seeking to make it to the quarter-finals for the third year in a row, having won the competition in 2012 and reached the last four last season. Shakhtar are hoping to reach the last eight for only the second time in their history - the Ukrainians last qualified for the quarter-finals in 2011.
Brazilian midfielder Bernard (r.) is the only player Shakhtar coach Mircea Lucescu is unable to rely upon in Lviv on Tuesday night. Luiz Adriano, top scorer in this season's Champions League with nine goals, is fit and should lead the Pitmen's attack.
Bayern were forced to leave Gianluca Gaudino at home due to illness, but Xabi Alonso (l.), who missed Saturday's 8-0 win over Hamburger SV with a thigh strain, did board the flight for Lviv and could return. Rafinha and Franck Ribery were also on board after making their first appearance of 2015 against Hamburg.
Cristiano Ronaldo netted a tournament record nine goals in the group stage as Real Madrid CF marched to the title last season, but his record lasted only one year before it was matched by Luiz Adriano (r.). The Brazilian also became only the second player after Lionel Messi to score five in a single match with his one-man-show against FC BATE Borisov in October.
Arjen Robben was at it again at the weekend, scoring two sensational solo goals - one with his left foot, the other with his right - in the demolition of HSV. "I’ve done a lot already and as long as I’m enjoying it and I’m really fit I will continue and, hopefully, keep improving," said the Dutchman.
Darijo Srna (Shakhtar captain): "It’s great to play one of the best teams in the world. We’re not afraid."
Robben: "I don’t like people talking about the quarter- or semi-finals, or saying: ‘When will you meet Madrid or Barca?’ It’s Shakhtar first, and nothing more."
Bayern seem to have put their post-winter blues behind them with back-to-back Bundesliga wins ensuring they go into Tuesday’s game with a comfortable cushion at the top of the Bundesliga. Shakhtar have not had a competitive game since December, but they kept warm over the winter in Brazil and Spain, beating the likes of SC Internacional and Real Murcia CF in friendlies.
This is Bayern’s first meeting with Shakhtar, but not their first trip to Ukraine, where they have won only once in five clashes with FC Dynamo Kyiv. That win was in the 1994/95 Champions League group stage. Shakhtar don’t have the best of records against German opposition, having lost 4-0 away to Bayer Leverkusen (r.) in October 2013 and drawn 0-0 at home.
Shakhtar: Pyatov - Srna, Kucher, Rakytsky, Shevchuk - Douglas Costa, Fernando, Fred, Taison - Alex Teixeira - Luiz Adriano
Bayern: Neuer - Rafinha, Boateng, Dante, Juan Bernat - Götze, Schweinsteiger, Alaba - Robben, Müller, Ribery