Any process in which a virus stops, prevents, or reduces the frequency, rate or extent of host JAK1 (Janus Kinase 1) activity. In the host, binding of a ligand to a receptor triggers activation of JAK proteins, which phosphorylate tyrosine residues on the receptor creating sites for STAT proteins to bind, which are in turn phosphorylated and activated by JAK proteins. By blocking JAK1 activity, many viruses block the host signal transduction pathway.