The structure-specific Mus81-Eme1/Mms4 endonuclease contributes importantly to DNA repair and genome integrity maintenance. Here, using budding yeast, we have studied its function and regulation during the cellular response to DNA damage and show that this endonuclease is necessary for successful chromosome replication and cell survival in the presence of DNA lesions that interfere with replication fork progression. On the contrary, Mus81-Mms4 is not required for coping with replicative stress originated by acute treatment with hydroxyurea (HU), which causes fork stalling. Despite its requirement for dealing with DNA lesions that hinder DNA replication, Mus81-Mms4 activation is not induced by DNA damage at replication forks. Full Mus81-Mms4 activity is only acquired when cells finish S-phase and the endonuclease executes its function after the bulk of genome replication is completed. This post-replicative mode of action of Mus81-Mms4 limits its nucleolytic activity during S-phase, thus avoiding the potential cleavage of DNA substrates that could cause genomic instability during DNA replication. At the same time, it constitutes an efficient fail-safe mechanism for processing DNA intermediates that cannot be resolved by other proteins and persist after bulk DNA synthesis, which guarantees the completion of DNA repair and faithful chromosome replication when the DNA is damaged.