Upon recognition of microbial DNA or self-DNA, the cyclic-GMP-AMP synthase (cGAS) of the host catalyzes the production of the cyclic dinucleotide cGAMP. cGAMP is the main activator of STING, stimulator of interferon genes, leading to interferon synthesis through the STING-TBK1-IRF3 pathway. STING is also a hub for activation of NF-κB and autophagy. The present review details the striking similarities between T and B cell responses in severe coronavirus disease 2019 (COVID-19) and both animal or human models of STING gain of function (SAVI syndromes: STING-associated vasculopathy with onset in infancy). Those similarities may be further clues for a delayed activation of STING in severe COVID-19 patients, due to DNA damages following severe acute respiratory syndrome coronaviruses (SARS-CoV-2) infection and unusual role of STING in SARS-CoV-2 control. In early stages, Th2 differentiation are noticed in both severe COVID-19 and SAVI syndromes; then, CD4+ and CD8+ T cells functional exhaustion/senescent patterns due to TCR hyper-responsiveness are observed. T cell delayed over-responses can contribute to pneumonitis and delayed cytokine secretion with over-production of IL-6. Last, STING over-activation induces progressive CD4+ and CD8+ T lymphopenia in SAVI syndromes, which parallels what is observed in severe COVID-19. ACE2, the main receptor of SARS-CoV-2, is rarely expressed in immune cells, and it has not been yet proven that some human lymphocytes could be infected by SARS-CoV-2 through CD147 or CD26. However, STING, expressed in humans T cells, might be triggered following excessive transfer of cGAMP from infected antigen presenting cells into activated CD4+ and CD8+ T cells lymphocytes. Indeed, those lymphocytes highly express the cGAMP importer SLC19A1. Whereas STING is not expressed in human B cells, B cells counts are much less affected, either in COVID-19 or SAVI syndromes. The recognition of delayed STING over-activation in severe COVID-19 patients could prompt to target STING with specific small molecules inhibitors already designed and/or aspirin, which inhibits cGAS.