Muguruza won at Roland Garros in 2016 and also triumphed at last year's WTA Finals.
However, the world No.10 fell to the unseeded Kanepi in her first-round match on Sunday.
Muguruza, seeded No.10, lost 2-6 6-3 6-4 to the Estonian world No.46, who recorded her 10th career win at a Major over a player ranked inside the top 10.
Kanepi, who is the oldest player in the women's main draw, also extended her brilliant record against seeds in grand slam tournaments, having now won 19 such matches.
Among active players, only Serena Williams (29), her sister Venus (22) and French Open 10th seed Victoria Azarenka (21) have more such wins.
She will now play Brazilian Beatriz Haddad Maia in the second round.