The emergence of begomoviruses (whitefly-transmitted viruses classified in the genus Begomovirus, family Geminiviridae) in Brazil probably occurred by horizontal transfer from non-cultivated plants after the introduction of Bemisia tabaci MEAM1. The centre of diversity of Euphorbia heterophylla (Euphorbiaceae) is located in Brazil and Paraguay, where it is an invasive species in soybean and other crops. Reports of possible begomovirus infection of E. heterophylla in Brazil date back to the 1950s. In 2011, Euphorbia yellow mosaic virus (EuYMV) was described in symptomatic plants collected in the Brazilian state of Goiás. Here we assess the genetic variability and population structure of begomoviruses infecting E. heterophylla in samples collected throughout nine Brazilian states from 2009 to 2014. A total of 158 and 57 haplotypes were compared in DNA-A and DNA-B datasets, respectively. Analysis comparing population structure in a large sampled area enabled us to differentiate two subpopulations. Further, the application of discriminant analysis of principal components allowed the differentiation of six subpopulations according to sampling locations and in agreement with phylogenetic analysis. In general, negative selection was predominant in all six subpopulations. Interestingly, we were able to reconstruct the phylogeny based on the information from the 23 sites that contributed most to the geographical structure proposed, demonstrating that these polymorphisms hold supporting information to discriminate between subpopulations. These sites were mapped in the genome and compared at the level of amino acid changes, providing insights into how genetic drift and selection contribute to maintain the patterns of begomovirus population variability from a geographical structuring point of view.