Posttranslational modifications (PTMs) of tubulin specify microtubules for specialized cellular functions and comprise what is termed a "tubulin code." PTMs of histones comprise an analogous "histone code," although the "readers, writers, and erasers" of the cytoskeleton and epigenome have heretofore been distinct. We show that methylation is a PTM of dynamic microtubules and that the histone methyltransferase SET-domain-containing 2 (SETD2), which is responsible for H3 lysine 36 trimethylation (H3K36me3) of histones, also methylates α-tubulin at lysine 40, the same lysine that is marked by acetylation on microtubules. Methylation of microtubules occurs during mitosis and cytokinesis and can be ablated by SETD2 deletion, which causes mitotic spindle and cytokinesis defects, micronuclei, and polyploidy. These data now identify SETD2 as a dual-function methyltransferase for both chromatin and the cytoskeleton and show a requirement for methylation in maintenance of genomic stability and the integrity of both the tubulin and histone codes.