In this article, we demonstrate an acoustofluidic device for cell lysis using the acoustic streaming effects induced by acoustically oscillating sharp-edged structures. The acoustic streaming locally generates high shear forces that can mechanically rupture cell membranes. With the acoustic-streaming-derived shear forces, our acoustofluidic device can perform cell lysis in a continuous, reagent-free manner, with a lysis efficiency of more than 90% over a range of sample flow rates. We demonstrate that our acoustofluidic lysis device works well on both adherent and non-adherent cells. We also validate it using clinically relevant samples such as red blood cells infected with malarial parasites. Additionally, the unique capability of our acoustofluidic device was demonstrated by performing downstream protein analysis and gene profiling without additional washing steps post-lysis. Our device is simple to fabricate and operate while consuming a relatively low volume of samples. These advantages and other features including the reagent-free nature and controllable lysis efficiency make our platform valuable for many biological and biomedical applications, particularly for the development of point-of-care platforms.