Patterning of developing tissues arises from a number of mechanisms, including cell shape change, cell proliferation, and cell sorting from differential cohesion or tension. Here, we reveal that differences in cell motility can also lead to cell sorting within tissues. Using mosaic engineered mammary epithelial tubules, we found that cells sorted depending on their expression level of the membrane-anchored collagenase matrix metalloproteinase (MMP)-14. These rearrangements were independent of the catalytic activity of MMP14 but absolutely required the hemopexin domain. We describe a signaling cascade downstream of MMP14 through Rho kinase that allows cells to sort within the model tissues. Cell speed and persistence time were enhanced by MMP14 expression, but only the latter motility parameter was required for sorting. These results indicate that differential directional persistence can give rise to patterns within model developing tissues.