"The Buddha asked his monks to keep their heads and faces shaved and nuns to keep their heads shaved, probably for hygienic reasons and to lessen vanity (Vin.II,207). Nuns were expected to shave their under-arm and pubic hair which was a sign of respectability in women (Vin.III,260). Monks were also asked to cut the hair in their noses if it got too long so as to avoid having a curious or unpleasant appearance(Vin.II,134)."source
Eyebrows aren't specifically mentioned, but I think the nose-hair clause (!) would apply.