The 24-year-old Aouar has French and Algerian nationality and decided to make the switch to play for Algeria last week. He posted a photo of himself wearing Algeria's national jersey on Instagram.
"L'OL (Lyon) offers its support to @HoussemAouar along with all the other people who are victims of racism and discriminatory acts because of their origins and life choices," Lyon posted on Twitter, adding that it "condemns hatred."
Aouar played once for France in a friendly match against Ukraine three years ago. He has also represented France at the youth level and with the under-21 team.
Aouar, who was jeered by some of his home fans during a league game against Nantes last Friday, posted a screenshot on Instagram on Wednesday showing some of the racist abuse he has been receiving.
Last November, Aouar posted a photo of himself holding up a red card on Twitter to join the campaign against cyber harassment.
He is one of several players to have come through Lyon's renowned youth academy and has scored 46 goals in 251 games for Lyon.
His contract with the seven-time French champions ends in June.