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 by stopping, preventing, or reducing the frequency, rate or extent of the introduction of a phosphate group to a tyrosine residue of a STAT2 protein. For example, the measles virus V protein inhibits tyrosine phosphorylation of STAT2, thereby preventing STAT2 activation.