The demand to understand the mechanical properties of cells from biomedical, bioengineering, and clinical diagnostic fields has given rise to a variety of research studies. In this context, how to use lab-on-a-chip devices to achieve accurate, high-throughput, and non-invasive acquisition of the mechanical properties of cells has become the focus of many studies. Accordingly, we present a comprehensive review of the development of the measurement of mechanical properties of cells using passive microfluidic mechanisms, including constriction channel-based, fluid-induced, and micropipette aspiration-based mechanisms. This review discusses how these mechanisms work to determine the mechanical properties of the cell as well as their advantages and disadvantages. A detailed discussion is also presented on a series of typical applications of these three mechanisms to measure the mechanical properties of cells. At the end of this article, the current challenges and future prospects of these mechanisms are demonstrated, which will help guide researchers who are interested to get into this area of research. Our conclusion is that these passive microfluidic mechanisms will offer more preferences for the development of lab-on-a-chip technologies and hold great potential for advancing biomedical and bioengineering research studies.