In budding yeast, chromatin mobility increases after a DNA double-strand break (DSB). This increase is dependent on Mec1, the yeast ATR kinase, but the targets responsible for this phenomenon are unknown. Here we report that the Mec1-dependent phosphorylation of Cep3, a kinetochore component, is required to stimulate chromatin mobility after DNA breaks. Cep3 phosphorylation counteracts a constraint on chromosome movement imposed by the attachment of centromeres to the spindle pole body. A second constraint, imposed by the tethering of telomeres to the nuclear periphery, is also relieved after chromosome breakage. A non-phosphorylatable Cep3 mutant that impairs DSB-induced chromatin mobility is proficient in DSB repair, suggesting that break-induced chromatin mobility may be dispensable for homology search. Rather, we propose that the relief of centromeric constraint promotes cell cycle arrest and faithful chromosome segregation through the engagement of the spindle assembly checkpoint.