During mitosis, chromatin condensation shapes chromosomes as separate, rigid, and compact sister chromatids to facilitate their segregation. Here, we show that, unlike wild-type yeast chromosomes, non-chromosomal DNA circles and chromosomes lacking a centromere fail to condense during mitosis. The centromere promotes chromosome condensation strictly in cis through recruiting the kinases Aurora B and Bub1, which trigger the autonomous condensation of the entire chromosome. Shugoshin and the deacetylase Hst2 facilitated spreading the condensation signal to the chromosome arms. Targeting Aurora B to DNA circles or centromere-ablated chromosomes or releasing Shugoshin from PP2A-dependent inhibition bypassed the centromere requirement for condensation and enhanced the mitotic stability of DNA circles. Our data indicate that yeast cells license the chromosome-autonomous condensation of their chromatin in a centromere-dependent manner, excluding from this process non-centromeric DNA and thereby inhibiting their propagation.