The Premier League champions, who reached last season's European final, will face Madrid at home before travelling to Bayern. They will also meet Borussia Dortmund and Napoli as they look to secure a place in the top eight and automatic qualification for the last 16.
Manchester City and Aston Villa have also been given difficult assignments, with both clubs set to face defending champions Paris Saint-Germain. Villa's home meeting with PSG will be a repeat of the recent Super Cup, which the French side won 2-1 in Salzburg.
Villa will also travel to Barcelona and host Borussia Dortmund, while City's schedule includes an away game against Barcelona as well as meetings with Sporting CP, Porto, Napoli and RB Leipzig.
Liverpool will travel to Inter Milan and host Atletico Madrid among their eight league-phase fixtures. Manchester United will also meet Atletico, while Bayern Munich will visit Old Trafford.
Premier League clubs' opponents
Arsenal: Real Madrid (H), Bayern Munich (A), Borussia Dortmund (H), Real Betis (A), Lille (H), Napoli (A), Sabah (H), Slavia Prague (A)
Aston Villa: Barcelona (A), PSG (H), Borussia Dortmund (H), Club Brugge (A), Fenerbahce (H), Galatasaray (A), Viking (H), Slavia Prague (A)
Liverpool: Inter Milan (A), Atletico Madrid (H), FC Porto (H), Club Brugge (A), Villarreal (H), Fenerbahce (A), Lens (H), LASK (A)
Manchester City: PSG (H), Barcelona (A), Sporting CP (H), Porto (A), Napoli (H), RB Leipzig (A), AEK Athens (H), Lens (A)
Manchester United: Atletico Madrid (A), Bayern Munich (H), Roma (H), Sporting CP (A), RB Leipzig (H), Villarreal (A), Sabah (H), Como (A)
Champions League schedule
The league phase begins from September 8-10, with the opening six rounds running through to December.
The competition resumes in January, with the eighth and final league-phase round scheduled for January 27.
The top eight teams in the final table will advance directly to the round of 16 in March. Teams finishing ninth to 24th will enter the knockout play-offs, where they will compete for the remaining eight last-16 places.
Clubs finishing from 25th to 36th will be eliminated.
Exact dates and kick-off times for each fixture are due to be confirmed on Saturday.
Four clubs prepare for their debut
This season's competition will also welcome four Champions League newcomers.
Como, coached by former Arsenal and Chelsea midfielder Cesc Fabregas, will make their debut alongside Austria's LASK, Norway's Viking and Azerbaijan's Sabah.
There is also a landmark coaching first, with former Manchester City midfielder Yaya Toure becoming the first African coach to lead a team into the main Champions League draw after guiding Slovakian champions Slovan Bratislava through the qualifying play-offs.