The Red Devils came back late on to beat Bayern in the 1999 final and complete the treble, but the German champions came out on top in the sides’ last Champions League encounter in the 2014 quarter-finals.
Erik ten Hag’s United side will also be up against Rasmus Hojlund’s first professional club FC Copenhagen of Denmark, as well as Turkish side Galatasaray in Group A.
The draw pits Kane against United, a club long linked with signing him from Tottenham before Bayern completed a deal for him earlier this summer.
Bayern chief executive Jan-Christian Dreesen said: “This is and will remain the pinnacle of club football. Manchester United is one of the really big names in European football, with whom we have a number of historic duels.
“Since we won the title in Lisbon in 2020, we have now finished three times in the quarter-finals. It is our great wish that things go further this season.”
Newcastle face a hugely difficult task as they prepare to return to the competition for the first time since 2002-03.
Eddie Howe’s side finished fourth in the Premier League last season and they have been paired with three European heavyweights – seven-time Champions League winners AC Milan, 1997 winners Borussia Dortmund and 2020 finalists Paris St Germain in Group F.
“Wow, what a group!” Newcastle chief executive Darren Eales said.
“It’s a super group of death, three great teams – PSG, Dortmund, the yellow wall, and AC Milan.
“In 2003 we had almost 10,000 Geordies over in the wonderful city of Milan – and I don’t think I’ve ever seen a Mackem in Milan – so it’s going to be exciting.
“PSG are footballing royalty and Dortmund are a great football club. The noise at St James’ Park for that first game is going to be something special.
“We had a great season last season and we’re not here to make up the numbers.
“We’ve got six great games ahead of us and we’re really going to give it our all. We want our fans to dream and have a draw and a group we can get excited about.”
The Magpies’ sporting director Dan Ashworth said it was an “amazing” draw and added: “It’s been a 20-year wait to play against the top teams in Europe and we certainly got that in our group, didn’t we?
“It’s very exciting, brilliant for the fans, brilliant for the staff, it’s what the Champions League is all about.”
Paris St Germain president Nasser Al Khelaifi said it was a “tough” draw for his team but added: “It’s the best club competition in the world. Everybody wants to play, so don’t complain – these are the best matches we can ever play.
“I think it will be a real motivation for the players, for the staff, for the coach, and it’s fantastic.”
Holders Manchester City face German side RB Leipzig for the third successive season in the Champions League after being pitted against Josko Gvardiol’s former club in Thursday’s group stage draw in Monaco.
City hammered Leipzig 7-0 in the second leg of their last-16 tie last season, having also beaten them 6-3 in the group stage the season before last.
Also in City’s group are Serbian champions Red Star Belgrade, winners of the European Cup in 1991, and Swiss side Young Boys, with Pep Guardiola’s side seeking to build on their success in Istanbul last season by retaining the title at Wembley next June.
Arsenal, back in the Champions League for the first time since 2016-17, face seven-time Europa League winners Sevilla in Group B.
The Gunners, who were runners-up behind City in last season’s Premier League, are also up against Dutch side PSV Eindhoven and French team Lens.
Scottish champions Celtic were placed in Group E alongside Eredivisie champions Feyenoord, Atletico Madrid of Spain and Italian side Lazio.
The first round of group games will be played on September 19 and 20.
This marks the final season of the group stage in its familiar form. From next season, 36 teams will take part in a league phase, where they will play eight matches on a seeded ‘Swiss system’.