As the Zika virus protease is an essential and well-established target for the development of antiviral agents, we biochemically screened for inhibitors using a purified recombinantly expressed form of this enzyme. As a result, we were able to identify 10 new Zika virus protease inhibitors. These compounds are natural products and showed strong inhibition in the biochemical assays. Inhibitory constants values for the compounds ranged from 5 nM to 8 μM. Among the most potent inhibitors are flavonoids like irigenol hexa-acetate (K =0.28 μM), katacine (K =0.26 μM), theaflavin gallate (K =0.40 μM) and hematein (K =0.33 μM). Inhibitors from other groups of natural products include sennoside A (K =0.19 μM) and gossypol (K =0.70 μM). Several of the obtained compounds are known for their beneficial health effects and have acceptable pharmacokinetic characteristics. Thus, they could be of interest as lead compounds for the development of important and essential Zika antiviral drugs.