Seven different countries had clubs in the draw, though there were no representatives from Germany or Italy, after the big five European countries provided all of the quarterfinalists last season.
UEFA also made the semifinal draw pairings, with a possible clash between Chelsea and Barça in the offing if both overcome their quarterfinal opponents.
Chelsea were knocked out in the semifinals by Barça last year and lost 4-0 to the Spanish side in the 2021 final.
With Hayes set to leave the London side at the end of the season, this is her last chance to win the only trophy that has eluded her during her time at the club.
The quarterfinal first-legs are scheduled for March 19-20 and the second-legs will take place on March 27-28.
The first-leg of the semifinals will be played on April 20-21, with the return legs on April 27-28.
Women’s Champions League quarterfinal draw
Barcelona v SK Brann
Lyon v Benfica
Chelsea v Ajax
Paris St Germain v BK Hacken
Women’s Champions League semifinal draw
SK Brann/Barcelona v Ajax/Chelsea
Benfica/Lyon v Hacken/PSG
Information from the Associated Press contributed to this report.