Flick's announcement capped a turbulent week for Bayern, who bounced back from their Champions League quarter-final exit at the hands of PSG on Tuesday.
Flick, who has a contract with the club to 2023, said he told the team he had informed the club of his wish to leave.
The absence of Robert Lewandowski has left Bayern with a huge hole in attack, compounded by the unavailability of Serge Gnabry, who is isolating after contracting Covid-19.
The draw trims Bayern's lead at the top of the Bundesliga table to five points ahead of second-placed RB Leipzig, who romped to a 4-1 win at Werder Bremen.
Pernille Harder gave Chelsea the lead against her former team in Budapest — where both legs were played — with a 27th-minute penalty and four minutes later Sam Kerr effectively put the tie out of the Germans' reach.
Lyon sit a point behind Paris Saint-Germain in the French league and on Wednesday the clubs take their rivalry into Europe as they meet in the first leg of their quarter-final.
German Cup: RB Leipzig through to semis with victory over Wolfsburg; Holstein Kiel also reach last-four
After Poulsen opened the scoring, South Korea striker Hwang came off the bench to hit a late second goal and seal a semi-final berth alongside Borussia Dortmund and Kiel.
European football matchday: Barcelona host Sevilla in semi-finals of Copa del Rey; Ibrahimovic-less AC Milan play Inter
A look at what’s happening in European football on Wednesday
Leipzig fought back with second-half goals by Christopher Nkunku and Yussuf Poulsen before Sorloth's winning header in the 93rd minute after Gladbach had led 2-0 at half-time.
Bundesliga: Wolfsburg strengthen chances of Champions League qualification with 3-0 win over Arminia Bielefeld
Renato Steffen scored twice, and a rocket from Maximilian Arnold helped Wolfsburg move third ahead of rest of the 22nd round.
Bundesliga: Eintracht Frankfurt move to third spot with win over Cologne; Wolfsburg held by Borussia Monchengladbach
Wolfsburg extended their run of games without conceding to six across all competitions but saw the end of its five-game winning run.
Bundesliga: Wolfsburg beat Freiburg to rise to third in table; Marius Wolf's brace helps Cologne win
Wolfsburg climbed above Bayer Leverkusen, Borussia Dortmund and Eintracht Frankfurt to move firmly into contention for Champions League qualification.
Bayern Munich’s closest challengers, RB Leipzig and Bayer Leverkusen, both lost in the Bundesliga on Saturday to give the eight-time defending champions a chance to move seven points clear at the top.
The victory was Leverkusen's first in five league games and puts them second on goal difference, level on 32 points with RB Leipzig, who host Union Berlin on Wednesday.
For the second consecutive Saturday, Leipzig, who lost 3-1 last weekend at home to Borussia Dortmund, missed out on first place.
Bundesliga: Erling Haaland shines as Borussia Dortmund beat RB Leipzig; Schalke thrash Hoffenheim 4-0
Haaland is the first player to score 25 goals in his first 25 Bundesliga games and the 20-year-old has now netted 35 goals in 34 games in all competitions for Dortmund.
Bundesliga: Robert Lewandowski nets twice as Bayern Munich come from two behind; Jadon Sancho ends goal drought
Mainz's 2-0 half-time lead was wiped out within 10 minutes of the restart as Bayern netted five unanswered second-half goals at the Allianz Arena.
Bundesliga: Borussia Dortmund's Erling Haaland back in action as German top-flight league returns post winter break
Haaland has missed the last four league games and the last seven in all competitions after picking up a hamstring injury in early December.
Four Wolfsburg players missed out after positive coronavirus tests. Three more were in isolation because of close contact with their infected teammates. Coach Oliver Glasner named three reserve goalkeepers among his seven substitutes, with two of the keepers dressed as outfield players.
Poor defending let Hertha Berlin down in a 4-1 loss at Freiburg which leaves the big-spending Berlin team 14th in the 18-team league, and with one win in its last six games.