Although some Countries in South America have implemented laboratory and patient management protocols for the new coronavirus, the lack of access to basic sanitation and hygiene measures, as well as the lack of drugs and vaccines, has significantly interfered with the epidemiological mechanics of the virus, emphasizing its implications. Therefore, trying to understand the evolutionary aspects of the virus, emerges as another strategy that can help in the most varied measures of prophylaxis. In this work, we evaluated the levels of genetic diversity in 38 complete Genomes of SARS-CoV-2 from six countries in South America, using specific methodologies for paired FST, AMOVA, mismatch, demographic and spatial expansions, molecular diversity and for the time of evolutionary divergence. The analyses showed non-significant evolutionary divergences within and between the six countries, as well as a significant similarity to the time of genetic evolutionary divergence between all populations. Thus, it seems safe to affirm that we will find similar results for the other Countries of South America, reducing speculation about the existence of rapid and silent mutations that, although there are as we have shown in this work, do not increase, until this moment, the genetic variability of the Virus, a fact that would hinder the work with molecular targets for vaccines and drugs in general.