The malaria elimination programme in Kayin State (Myanmar) uses malaria posts for rapid detection and treatment, together with mass drug administration in high-transmission villages, which has reduced transmission by 97%. Here we examine the impact of control on parasite genomic parameters to inform future control efforts. Using 2,270 genome-sequenced Plasmodium falciparum infections from 283 malaria posts, sampled over 58 months (2015-2020), we find that parasite effective population size decreased over the study period, but there was minimal change in artemisinin resistance allele frequency until 2020, when just one predominant genotype (carrying kelch13-R561H) remained. We observed sustained localized transmission of unique parasite genotypes revealing transmission chains and positive correlations in parasite relatedness for ≤20 km. Mass drug administration resulted in parasite founder effects, providing genomic evidence for the efficacy of this control tool. These results reveal changes in population structure driven by control and rapid shifts in allele frequency in a parasite population close to elimination.