Peru has become one of the countries with the highest mortality rates from the current coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). To investigate early transmission events and the genomic diversity of SARS-CoV-2 isolates circulating in Peru in the early COVID-19 pandemic, we analyzed 3472 viral genomes, of which 149 were from Peru. Phylogenomic analysis revealed multiple and independent introductions of the virus likely from Europe and Asia and a high diversity of genetic lineages circulating in Peru. In addition, we found evidence for community-driven transmission of SARS-CoV-2 as suggested by clusters of related viruses found in patients living in different regions of Peru.