I think that traditional Buddhism and Communism have different views on the relationship between body and mind. Early Communism (orthodox Marxism) is materialist, while Buddhism is neither materialist nor idealist. Buddhism is also misunderstood as "atheistic". It is non-theistic, since it doesn't deny the existence of gods, but simply considers them irrelevant.
I do think, however, that the early Sangha resembles some of the voluntary communes of certain forms of Marxism, such as Marxist Anarchism. Early Zen Buddhist institutions are referred to as "Chan communes," where there was a shared distribution of labor, resources, etc..
But nothing in the teachings go so far as to proscribe this for everyone; far from it, since the Buddha didn't advocate having his monks control the world, set up a certain social order, etc.. Buddhist teachings are largely unconcerned with politics and the interpretation of them in the light of politics is largely a personal preference. Communism is an ideology which proscribes that the whole world be a certain way, to rectify injustice. Early Buddhist communism was established internally simply because it was the most practical.
The best things in life aren't things.