Asymmetric cell division gives rise to two daughter cells that inherit different determinants, thereby acquiring different fates. Polarized trafficking of endosomes containing fate determinants recently emerged as an evolutionarily conserved feature of asymmetric cell division to enhance the robustness of asymmetric cell fate determination in flies, fish and mammals. In particular, polarized sorting of signalling endosomes by an asymmetric central spindle contributes to asymmetric cell division in Drosophila melanogaster. However, how central spindle asymmetry arises remains elusive. Here we identify a moonlighting function of the Elongator complex—an established protein acetylase and tRNA methylase involved in the fidelity of protein translation—as a key factor for central spindle asymmetry. Elongator controls spindle asymmetry by stabilizing microtubules differentially on the anterior side of the central spindle. Accordingly, lowering the activity of Elongator on the anterior side using nanobodies mistargets endosomes to the wrong cell. Molecularly, Elongator regulates microtubule dynamics independently of its acetylation and methylation enzymatic activities. Instead, Elongator directly binds to microtubules and increases their polymerization speed while decreasing their catastrophe frequency. Our data establish a non-canonical role of Elongator at the core of cytoskeleton polarity and asymmetric signalling.