Currently, there is still no effective and definitive cure for the coronavirus disease 2019 (COVID-19) caused by the infection of the novel highly contagious severe acute respiratory syndrome virus (SARS-CoV-2), whose sudden outbreak was recorded for the first time in China in late December 2019. Soon after, COVID-19 affected not only the vast majority of China’s population but the whole world and caused a global health public crisis as a new pandemic. It is well known that viral infection can cause acute respiratory distress syndrome (ARDS) and, in severe cases, can even be lethal. Behind the inflammatory process lies the so-called cytokine storm (CS), which activates various inflammatory cytokines that damage numerous organ tissues. Since the first outbreak of SARS-CoV-2, various research groups have been intensively trying to investigate the best treatment options; however, only limited outcomes have been achieved. One of the most promising strategies represents using either stem cells, such as mesenchymal stem cells (MSCs)/induced pluripotent stem cells (iPSCs), or, more recently, using cell-free approaches involving conditioned media (CMs) and their content, such as extracellular vesicles (EVs) (e.g., exosomes or miRNAs) derived from stem cells. As key mediators of intracellular communication, exosomes carry a cocktail of different molecules with anti-inflammatory effects and immunomodulatory capacity. Our comprehensive review outlines the complex inflammatory process responsible for the CS, summarizes the present results of cell-free-based pre-clinical and clinical studies for COVID-19 treatment, and discusses their future perspectives for therapeutic applications.