Oxidative stress (OS) occurs when the production of reactive oxygen species (ROS) is not balanced by the body’s antioxidant defense system. OS can profoundly affect cellular health and function. ROS can have a profound negative impact on cells that undergo a predestined and time-regulated process of proliferation or differentiation, such as perinatal stem cells. Due to the large-scale employment of these immunotolerant stem cells in regenerative medicine, it is important to reduce OS to prevent them from losing function and increase their application in the regenerative medicine field. This goal can be achieved through a variety of strategies, such as the use of antioxidants and other compounds that can indirectly modulate the antioxidant defense system by enhancing cellular stress response pathways, including autophagy and mitochondrial function, thereby reducing ROS levels. This review aims to summarize information regarding OS mechanisms in perinatal stem cells and possible strategies for reducing their deleterious effects.