The draw was made on Friday and means there is an all-Spanish tie in the last eight which should prompt plenty of interest.
The two clubs set an attendance record for women’s football in March when they met at the Wanda Metropolitano in front of a crowd of 60,739.
The winner of their quarter-final clash will go on to face Glasgow City or Wolfsburg for a place in the final.
Barcelona Femeni have never won the Women’s Champions League and were beaten finalists last season, going down 4-1 to champions Lyon.
They thrashed Atletico 6-1 back in September in the league and are currently top of the table.
Arsenal v Paris St-Germain
Glasgow City v Wolfsburg
Atletico Madrid v Barcelona
Lyon v Bayern Munich
Arsenal or Paris St-Germain v Lyon or Bayern Munich
Glasgow City or Wolfsburg v Atletico Madrid or Barcelona
The first legs will be played on the weekend of 24-25 March 2020 with the second legs set for 1-2 April.