Due to the presence of the ACE2 receptor in different tissues (nasopharynx, lung, nervous tissue, intestine, liver), the COVID-19 disease involves several organs in our bodies. SARS-CoV-2 is able to infect different cell types, spreading to different districts. In the host, an uncontrolled and altered immunological response is triggered, leading to cytokine storm, lymphopenia, and cellular exhaustion. Hence, respiratory distress syndrome (ARDS) and systemic multi-organ dysfunction syndrome (MODS) are established. This scenario is also reflected in the composition of the microbiota, the balance of which is regulated by the interaction with the immune system. A change in microbial diversity has been demonstrated in COVID-19 patients compared with healthy donors, with an increase in potentially pathogenic microbial genera. In addition to other symptoms, particularly neurological, the occurrence of dysbiosis persists after the SARS-CoV-2 infection, characterizing the post-acute COVID syndrome. This review will describe and contextualize the role of the immune system in unbalance and dysbiosis during SARS-CoV-2 infection, from the acute phase to the post-COVID-19 phase. Considering the tight relationship between the immune system and the gut–brain axis, the analysis of new, multidistrict parameters should be aimed at understanding and addressing chronic multisystem dysfunction related to COVID-19.