N6-methyladenosine (m6A) methylation is an abundant modification in eukaryotic mRNAs. Accumulating evidence suggests a role for RNA m6A methylation in various aspects of cancer biology. In this study, we aimed to explore the biological role of RNA m6A modification in tumor metastasis and to identify novel therapeutic strategies for esophageal squamous cell carcinoma (ESCC). Integration of genome-wide CRISPR/Cas9 functional screening with highly invasive and metastatic ESCC subline models led to the identification of METTL3, the catalytic subunit of the N6-adenosine-methyltransferase complex, as a promoter of cancer metastasis. METTL3 expression was upregulated in ESCC tumors and metastatic tissues. In vitro and in vivo experiments indicated that METTL3 increased m6A in EGR1 mRNA and enhanced its stability in a YTHDF3-dependent manner, activating EGR1/Snail signaling. Investigation into regulation of METTL3 expression found that KAT2A increased H3K27 acetylation levels in the METTL3 promoter region and activated transcription of METTL3 while SIRT2 exerted the opposite effects. Molecular docking and computational screening in a Food and Drug Administration (FDA)-approved compound library consisting of 1,443 small molecules identified compounds targeting METTL3 to suppress cancer metastasis. Elvitegravir, originally developed to treat human immunodeficiency virus (HIV) infection, suppressed metastasis by directly targeting METTL3 and enhancing its STUB1-mediated proteasomal degradation. Overall, RNA m6A modifications are important in cancer metastasis, and targeting METTL3 with elvitegravir has therapeutic potential for treating ESCC.