First of all, the Buddha did not envision an ideal human society, but the end of human society or rather: the end of everything human, which means suffering in the first place. Therefore, except for the rules that govern the life and community of monks and nuns for the time being, i.e. until enlightenment, there is no social teaching in the original word of the Buddha. So here, in the social sphere, my answer would be a straight no.
In later Mahayana Buddhism, though, the focal point shifts away from individual enlightenment, the new ideal being no more the Arhat, who achieves enlightenment for himself, but the Bodhisattva, who postpones his own enlightenment and strives to help and enlighten all other beings first. So in this stage, there is a social teaching, which does not contradict communism, I guess.
But maybe it would be useful, if you could specify exactly which tenets of communism/marxism you are having in mind, since for example quite obviously, there is no arguing on an economic basis in Buddhism. I guess, you did expect that.
There are two more things which come to my mind. First of all, again for early Buddhism, it denied the reality of class boundaries, which were in this specific context, the caste boundaries. The hierarchy within the order was based on age of service, i.e. time elapsed since ordination and there are stories from early Buddhism where hierarchies were turned upside down, the former low-caste dark-skin servant of some high-class person being all of a sudden his preceptor.
The other is a point where Buddhism is maybe much better compatible with marxism than any other religion could ever be: Buddhism denies the existence of the soul, of an all-powerful creator-god, rather it emphasizes cause and effect and a scientific approach to reality. This is not totally clear to me, but maybe even the mind can be seen as material.