The dynamic nature of genome organization impacts critical nuclear functions including the regulation of gene expression, replication, and DNA damage repair. Despite significant progress, the mechanisms responsible for reorganization of the genome in response to cellular stress, such as aberrant DNA replication, are poorly understood. Here, we show that fission yeast cells carrying a mutation in the DNA-binding protein Sap1 show defects in DNA replication progression and genome stability and display extensive changes in genome organization. Chromosomal regions such as subtelomeres that show defects in replication progression associate with the nuclear envelope in sap1 mutant cells. Moreover, high-resolution, genome-wide chromosome conformation capture (Hi-C) analysis revealed prominent contacts between telomeres and chromosomal arm regions containing replication origins proximal to binding sites for Taz1, a component of the Shelterin telomere protection complex. Strikingly, we find that Shelterin components are required for interactions between Taz1-associated chromosomal arm regions and telomeres. These analyses reveal an unexpected role for Shelterin components in genome reorganization in cells experiencing replication stress, with important implications for understanding the mechanisms governing replication and genome stability.