Genome-wide association studies of late-onset Alzheimer’s disease (AD) have highlighted the importance of variants associated with genes expressed by the innate immune system in determining risk for AD. Recently, we and others have shown that genes associated with variants that confer risk for AD are significantly enriched in transcriptional networks expressed by amyloid-responsive microglia. This allowed us to predict new risk genes for AD, including the interferon-responsive oligoadenylate synthetase 1 (OAS1). However, the function of OAS1 within microglia and its genetic pathway are not known. Using genotyping from 1,313 individuals with sporadic AD and 1,234 control individuals, we confirm that the OAS1 variant, rs1131454, is associated with increased risk for AD and decreased OAS1 expression. Moreover, we note that the same locus was recently associated with critical illness in response to COVID-19, linking variants that are associated with AD and a severe response to COVID-19. By analysing single-cell RNA-sequencing (scRNA-seq) data of isolated microglia from APPNL-G-F knock-in and wild-type C57BL/6J mice, we identify a transcriptional network that is significantly upregulated with age and amyloid deposition, and contains the mouse orthologue Oas1a, providing evidence that Oas1a plays an age-dependent function in the innate immune system. We identify a similar interferon-related transcriptional network containing OAS1 by analysing scRNA-seq data from human microglia isolated from individuals with AD. Finally, using human iPSC-derived microglial cells (h-iPSC-Mg), we see that OAS1 is required to limit the pro-inflammatory response of microglia. When stimulated with interferon-gamma (IFN-γ), we note that cells with lower OAS1 expression show an exaggerated pro-inflammatory response, with increased expression and secretion of TNF-α. Collectively, our data support a link between genetic risk for AD and susceptibility to critical illness with COVID-19 centred on OAS1 and interferon signalling, a finding with potential implications for future treatments of both AD and COVID-19, and the development of biomarkers to track disease progression.