Phylogenetics has a crucial role in genomic epidemiology. Enabled by unparalleled volumes of genome sequence data generated to study and help contain the COVID-19 pandemic, phylogenetic analyses of SARS-CoV-2 genomes have shed light on the virus’s origins, spread, and the emergence and reproductive success of new variants. However, most phylogenetic approaches, including maximum likelihood and Bayesian methods, cannot scale to the size of the datasets from the current pandemic. We present ‘MAximum Parsimonious Likelihood Estimation’ (MAPLE), an approach for likelihood-based phylogenetic analysis of epidemiological genomic datasets at unprecedented scales. MAPLE infers SARS-CoV-2 phylogenies more accurately than existing maximum likelihood approaches while running up to thousands of times faster, and requiring at least 100 times less memory on large datasets. This extends the reach of genomic epidemiology, allowing the continued use of accurate phylogenetic, phylogeographic and phylodynamic analyses on datasets of millions of genomes.