The molecular epidemiology of the virus and mapping helps understand the epidemics' evolution and apply quick control measures. This study provides genomic evidence of multiple severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) introductions into Sri Lanka and virus evolution during circulation. Whole-genome sequences of four SARS-CoV-2 strains obtained from coronavirus disease 2019 (COVID-19) positive patients reported in Sri Lanka during March 2020 were compared with sequences from Europe, Asia, Africa, Australia and North America. The phylogenetic analysis revealed that the sequence of the sample of the first local patient collected on 10 March, who contacted tourists from Italy, was clustered with SARS-CoV-2 strains collected from Italy, Germany, France and Mexico. Subsequently, the sequence of the isolate obtained on 19 March also clustered in the same group with the samples collected in March and April from Belgium, France, India and South Africa. The other two strains of SARS-CoV-2 were segregated from the main cluster, and the sample collected from 16 March clustered with England and the sample collected on 30 March showed the highest genetic divergence to the isolate of Wuhan, China. Here we report the first molecular epidemiological study conducted on circulating SARS-CoV-2 in Sri Lanka. The finding provides the robustness of molecular epidemiological tools and their application in tracing possible exposure in disease transmission during the pandemic.