A clash of heads with the United States defender Matt Miazga during Saturday's friendly left both players covered in blood.
Giroud received immediate medical attention from the French camp and was promptly replaced by compatriot Ousmane Dembele.
However, it seems the injury isn't as bad as first feared with Giroud expected to feature in some way for 'Les Bleus' during their first Group C match against Australia.
Deschamps told 'TF1' on Sunday: "Giroud has a beautiful cut of six centimetres but he should be ready".
The striker's injury was just one incident in an action-packed final friendly which saw France having to salvage a 1-1 draw against the inexperienced US side.