Centrosomes are the main microtubule-organizing centers in animal cells. Due to the semiconservative nature of centrosome duplication, the two centrosomes differ in age. In asymmetric stem cell divisions, centrosome age can induce an asymmetry in half-spindle lengths. However, whether centrosome age affects the symmetry of the two half-spindles in tissue culture cells thought to divide symmetrically is unknown. Here, we show that in human epithelial and fibroblastic cell lines centrosome age imposes a mild spindle asymmetry that leads to asymmetric cell daughter sizes. At the mechanistic level, we show that this asymmetry depends on a cenexin-bound pool of the mitotic kinase Plk1, which favors the preferential accumulation on old centrosomes of the microtubule nucleation-organizing proteins pericentrin, γ-tubulin, and Cdk5Rap2, and microtubule regulators TPX2 and ch-TOG. Consistently, we find that old centrosomes have a higher microtubule nucleation capacity. We postulate that centrosome age breaks spindle size symmetry via microtubule nucleation even in cells thought to divide symmetrically.