During replication arrest, the DNA replication checkpoint plays a crucial role in the stabilization of the replisome at stalled forks, thus preventing the collapse of active forks and the formation of aberrant DNA structures. How this checkpoint acts to preserve the integrity of replication structures at stalled fork is poorly understood. In Schizosaccharomyces pombe, the DNA replication checkpoint kinase Cds1 negatively regulates the structure-specific endonuclease Mus81/Eme1 to preserve genomic integrity when replication is perturbed. Here, we report that, in response to hydroxyurea (HU) treatment, the replication checkpoint prevents S-phase-specific DNA breakage resulting from Mus81 nuclease activity. However, loss of Mus81 regulation by Cds1 is not sufficient to produce HU-induced DNA breaks. Our results suggest that unscheduled cleavage of stalled forks by Mus81 is permitted when the replisome is not stabilized by the replication checkpoint. We also show that HU-induced DNA breaks are partially dependent on the Rqh1 helicase, the fission yeast homologue of BLM, but are independent of its helicase activity. This suggests that efficient cleavage of stalled forks by Mus81 requires Rqh1. Finally, we identified an interplay between Mus81 activity at stalled forks and the Chk1-dependent DNA damage checkpoint during S-phase when replication forks have collapsed.