Onconase^® (ONC) is a homolog of RNase A that is in clinical trials as a cancer chemotherapeutic agent. The toxicity of ONC and RNase A variants relies on their ability to evade the cytosolic ribonuclease inhibitor protein (RI) and degrade cellular RNA. We find that these ribonucleases are more toxic for more rapidly growing cells. The enhanced cytotoxicity does not arise from variation in the endogenous level of RI, which is virtually constant. Overproduction of RI diminishes the potency of toxic RNase A variants, but has no effect on the cytotoxicity of ONC. Thus, RI constrains the cytotoxicity of RNase A. These data provide new insights for the development of an optimal ribonuclease‐based cancer chemotherapy.