Glycosylation is critical for viral-host cell interactions in influenza A virus (IAV) infection, but we lack a comprehensive understanding of how IAV infection shapes the host glycoproteome and the implications of these changes. Here, we used a liquid chromatography-tandem mass spectrometry (LC-MS/MS) approach to perform proteomic, glycomic, and glycoproteomic characterisation of the dynamic subcellular responses to an in vitro time course infection of human A549 cells with two IAV strains (A/X-31, H3N2; and A/Puerto Rico/8/1934, H1N1). IAV infection resulted in only modest changes to the subcellular proteome, but robust and significant changes to the host secreted and organelle glycome and glycoproteome. Infection with either virus resulted in increased proportions of oligomannose, paucimannose, and phosphorylated glycans; reduced branching and length of complex glycans; and a widespread reduction in sialic acid across the N- and O-glyco(proteo)me. Reduced sialylation was consistent with desialylation of glycans by viral neuraminidase (NA), but with specific features of the glycan and protein controlling the extent of desialylation. Desialylation was greater when glycans were fucosylated; when the sialic acid was attached via an ⍺2,3 linkage or positioned on the ⍺3 arm; on larger, more complex glycans; and when present on proteins we infer are more accessible to IAV NA. Subtle, but prolonged activation of the unfolded protein response led to a doubling of oligomannose N-glycosylation. Glycans were shorter in infection, implicating IAV-induced disruption of Golgi glycoprotein flux as a mechanism to reduce host glycoprotein sialylation and promote virion release, independent of NA activity. Our data provide important insights into the host glycoproteome during influenza virus infection, furthering our understanding of how influenza NA acts upon host glycans, and how cell stresses in infection perturb key mediators of protein stability and function, cell signalling and immunity.