The Frenchman, who sent Sonny Bill Williams off in the second test against the Lions, didn't travel to Australia after suffering a calf injury while taking charge of a friendly between Bayonne and Racing 92 last weekend, L'Equipe reports.
Barnes was originally named as an assistant referee. Nigel Owens will replace Barnes for next weekend's test in Dunedin.
Garces is set to take charge of the October 7 clash between the All Blacks and South Africa in Cape Town.
Garces gave Williams a straight red card in the Wellington defeat, following a high no-arms tackle on Englishman Anthony Watson.