Branching microtubule nucleation is a key mechanism for mitotic and meiotic spindle assembly and requires the hetero-octameric augmin complex. Augmin recruits the major microtubule nucleator, the γ-tubulin ring complex, to pre-existing microtubules to direct the formation of new microtubules in a defined orientation. Although recent structural work has provided key insights into augmin’s structural organization, molecular details of its interaction with microtubules remain elusive. Here, we identify the minimal conserved microtubule-binding unit of augmin across species and demonstrate that the low-complexity microtubule-binding unit from D. melanogaster mediates microtubule binding predominantly via the calponin homology (CH) domain in Dgt6/HAUS6. Comparative sequence and functional analyses reveal a highly conserved architecture of the HAUS6 CH domain and variations in the importance of the HAUS8 N-terminus in microtubule binding. Using cryo-electron microscopy and molecular dynamics simulations, we show that the HAUS6 CH domain binds at the inter-protofilament groove between two adjacent β-tubulin subunits and thereby orients augmin on microtubules. Altogether, our findings reveal how augmin binds microtubules to pre-determine the branching angle during microtubule nucleation and thereby facilitates the rapid assembly of complex microtubule networks.