Moderate exercise combined with proper nutrition are considered protective factors against cardiovascular disease and musculoskeletal disorders. However, physical activity is known not only to have positive effects. In fact, the achievement of a good performance requires a very high oxygen consumption, which leads to the formation of oxygen free radicals, responsible for premature cell aging and diseases such as heart failure and muscle injury. In this scenario, a primary role is played by antioxidants, in particular by natural antioxidants that can be taken through the diet. Natural antioxidants are molecules capable of counteracting oxygen free radicals without causing cellular cytotoxicity. In recent years, therefore, research has conducted numerous studies on the identification of natural micronutrients, in order to prevent or mitigate oxidative stress induced by physical activity by helping to support conventional drug therapies against heart failure and muscle damage. The aim of this review is to have an overview of how controlled physical activity and a diet rich in antioxidants can represent a “natural cure” to prevent imbalances caused by free oxygen radicals in diseases such as heart failure and muscle damage. In particular, we will focus on sulfur-containing compounds that have the ability to protect the body from oxidative stress. We will mainly focus on six natural antioxidants: glutathione, taurine, lipoic acid, sulforaphane, garlic and methylsulfonylmethane.