Chemotherapeutic agents are part of the standard treatment algorithms for many malignancies; however, their application and dosage are limited by their toxic effects to normal tissues. Chemotherapy-induced toxicities can be long-lasting and may be incompletely reversible; therefore, causative therapies for chemotherapy-dependent side effects are needed, especially considering the increasing survival rates of treated cancer patients. Mesenchymal stem cells (MSCs) have been shown to exhibit regenerative abilities for various forms of tissue damage. Preclinical data suggest that MSCs may also help to alleviate tissue lesions caused by chemotherapeutic agents, mainly by establishing a protective microenvironment for functional cells. Due to the systemic administration of most anticancer agents, the effects of these drugs on the MSCs themselves are of crucial importance to use stem cell-based approaches for the treatment of chemotherapy-induced tissue toxicities. Here, we present a concise review of the published data regarding the influence of various classes of chemotherapeutic agents on the survival, stem cell characteristics and physiological functions of MSCs. Molecular mechanisms underlying the effects are outlined, and resulting challenges of MSC-based treatments for chemotherapy-induced tissue injuries are discussed.