The inhibition of arginase is of substantial interest for the treatment of various diseases of public health interest including cardiovascular diseases. Using an ex vivo experiment on rat aortic rings and an in vitro assay with liver bovine purified arginase, it was demonstrated that several polyphenolic extracts from Cyperus and Carex species possess vasorelaxant properties and mammalian arginase inhibitory capacities. Phytochemical studies performed on these species led to the identification of eight compounds, including monomers, dimers, trimers, and tetramers of resveratrol. The potential of these stilbenes as inhibitors of mammalian arginase was assessed. Five compounds, scirpusin B (5), ε-viniferin (4), cyperusphenol B (6), carexinol A (7), and the new compound virgatanol (1), showed significant inhibition of arginase, with percentage inhibition ranging from 70% to 95% at 100 μg/mL and IC50 values between 12.2 and 182.1 μM, confirming that these stilbenes may be useful for the development of new pharmaceutical products.