Centrosomes are the main microtubule‐organizing centers of animal cells. Although centrosome aberrations are common in tumors, their consequences remain subject to debate. Here, we studied the impact of structural centrosome aberrations, induced by deregulated expression of ninein‐like protein (NLP), on epithelial spheres grown in Matrigel matrices. We demonstrate that NLP‐induced structural centrosome aberrations trigger the escape (“budding”) of living cells from epithelia. Remarkably, all cells disseminating into the matrix were undergoing mitosis. This invasive behavior reflects a novel mechanism that depends on the acquisition of two distinct properties. First, NLP‐induced centrosome aberrations trigger a re‐organization of the cytoskeleton, which stabilizes microtubules and weakens E‐cadherin junctions during mitosis. Second, atomic force microscopy reveals that cells harboring these centrosome aberrations display increased stiffness. As a consequence, mitotic cells are pushed out of mosaic epithelia, particularly if they lack centrosome aberrations. We conclude that centrosome aberrations can trigger cell dissemination through a novel, non‐cell‐autonomous mechanism, raising the prospect that centrosome aberrations contribute to the dissemination of metastatic cells harboring normal centrosomes.