The short answer is "no." The economic systems employed by various Native American nations throughout time are too varied to be called communism, which itself is an economic system that cannot properly be said to exist before it was formalized theoretically in the 19th Century. The Native American nation most often associated with a sort of proto-communism is Tawantinsuyu, the Inca Empire. I'll let our Andean specialists handle the issues with that comparison if they happen to swing by this question.

However, there's a good chance that you're probably thinking of the nations from north of the Rio Grande, in what has become the US and Canada. In that case, the answer is still no.

There's a common myth that at the time of contact Native American cultures didn't have a concept of personal property, which is probably what is informing the comment you overheard. This stems from the fact that most nations in the Eastern Woodlands (where Anglo-colonists started showing in large numbers) didn't regard land as something individuals could own permanently. Land might belong to the whole polity or it might belong to a particular family line (usually a matrilineal clan). Individuals or families could claim a bit of that land for their use in farming, but when not being cultivated, the land typically reverted back to common use for either the clan or larger polity as appropriate.

But when that land was being cultivated, the products of the land belonged to the women who worked it, just as the products of the hunt usually belonged to the men who killed the animal. To give a specific example, let's look at the Cherokee in the late colonial period.

Cherokee towns at the time were surrounded by large fields, owned by the individual women or small groups of related women in the town. They were tended to by these women, and guarded by older women in nearby watchtowers. However, during the crucial planting and harvesting season the community, even the men, worked together to make sure everything got done in time. The community would go field by field, planting and harvest. But despite the community effort, the crop belonged to those who owned the field and went into their personal granaries. Mostly.

A portion of everyone's crop went into a communal granary, which was used to help support those who had had a poor harvest and needed assistance getting through the winter. If the communal granary ran empty before the end of winter, the women would organize a dance and the attendees would bring some of their own remaining stores to refill it.

So for the Cherokee, the products of one's agricultural labor was personal property, minus a small fraction that went to support a social safety net.

For another example, let's consider Tsenacommacah, the Powhatan Confederacy. Each local town and village had a leader known as a weroance, who in turn was subject to a regional weroance who oversaw a collection of towns from a regional center; these were subject to the mamanatowick, the leader of the entire confederacy. While even the mamanatowick was known to engage in common labor when he (or she, in the case of the last mamanatowick) had no official business to attend to, the common people were obligated to contribute labor to tend fields owned by their leaders, in addition to tending fields they owned as individual families. Men also contributed a sizable portion of the deer skins from their hunts. While a portion of these contributions enriched the weroances and the mamanatowick, they also served as a reserve from which the leadership could distribute as needed, both in the form of trade and as another form of social safety net in times of hardship.

Just to point out something general (beyond Reedstilt's fantastic reply)... Terminology is important. In popular (and political) culture, terms like "communist" or "socialist" are thrown around without any regard to their actual meaning. In many ways, they are simply used as a euphemism for "bad" or "un-American." This, of course, is thanks to the legacy (and effectiveness) of Cold War propaganda. However, it is anachronistic to call anyone in the eighteenth century or before a "communist," since communism as an ideology or mode of political economy did not exist.

Colonial and British societies in the seventeenth and eighteenth centuries were quite communitarian, especially in towns and villages. But being "communitarian" is not the same as being "communist." Historians have referred to this communitarianism as "corporatism." Effectively, it is meant to describe a form of "moral economy" that included practices like poor relief, price controls on necessary goods, and publicly-financed projects to benefit the public good (like building roads and bridges) as well as ideas that income equality was fundamental to actual political equality and that wage labor created a dependent citizenry while agricultural labor on one's own land created independent and virtuous individuals.