Antiviral activity has been demonstrated for different tannin-rich plant extracts. Since tannins of different classes and molecular weights are often found together in plant extracts and may differ in their antiviral activity, we have compared the effect against influenza A virus (IAV) of Hamamelis virginiana L. bark extract, fractions enriched in tannins of different molecular weights and individual tannins of defined structures, including pseudotannins. We demonstrate antiviral activity of the bark extract against different IAV strains, including the recently emerged H7N9, and show for the first time that a tannin-rich extract inhibits human papillomavirus (HPV) type 16 infection. As the best performing antiviral candidate, we identified a highly potent fraction against both IAV and HPV, enriched in high molecular weight condensed tannins by ultrafiltration, a simple, reproducible and easily upscalable method. This ultrafiltration concentrate and the bark extract inhibited early and, to a minor extent, later steps in the IAV life cycle and tannin-dependently inhibited HPV attachment. We observed interesting mechanistic differences between tannin structures: High molecular weight tannin containing extracts and tannic acid (1702 g/mol) inhibited both IAV receptor binding and neuraminidase activity. In contrast, low molecular weight compounds (<500 g/mol) such as gallic acid, epigallocatechin gallate or hamamelitannin inhibited neuraminidase but not hemagglutination. Average molecular weight of the compounds seemed to positively correlate with receptor binding (but not neuraminidase) inhibition. In general, neuraminidase inhibition seemed to contribute little to the antiviral activity. Importantly, antiviral use of the ultrafiltration fraction enriched in high molecular weight condensed tannins and, to a lesser extent, the unfractionated bark extract was preferable over individual isolated compounds. These results are of interest for developing and improving plant-based antivirals.