Any process in which a virus stops, prevents, or reduces the frequency, rate or extent of host STAT2 (signal transducer and activator of transcription-2) activity. STATs are SH2 domain-containing proteins which lie downstream of many signaling receptors. Upon phosphorylation by JAKs, STAT proteins hetero- or homo-dimerize and translocate to the nucleus to activate transcription of target genes.