The Reds were drawn with Paris Saint-Germain, SSC Napoli and Red Star Belgrade in Group C during Thursday's draw in Monaco.
Jürgen Klopp's team will begin their Champions League campaign with a home match against PSG on Tuesday September 18, before they then visit Napoli on Wednesday October 3.
Matchday three, on Wednesday October 24, will see Liverpool face Red Star at home, with the return meeting next up on Tuesday November 6.
The Reds will then take on PSG away on Wednesday November 28, before concluding Group C against Napoli at Anfield on Tuesday December 11.