Any process in which a virus stops, prevents, or reduces the frequency, rate or extent of host STAT1 (signal transducer and activator of transcription-1) activity by stopping, preventing, or reducing the frequency, rate or extent of the introduction of a phosphate group to a tyrosine residue of a STAT1 protein. For example, the measles virus V protein inhibits tyrosine phosphorylation of STAT1, thereby preventing STAT1 activation.