Mammalian cells have been widely used in bioreactors to produce biological products such as pharmaceutical materials. The productivity of such bioreactors is vastly affected by flow-induced cell damage in complicated flow environments, such as agitation-driven turbulence and oxygen bubble bursting at the interface between the culturing medium and air. However, there is no systematic approach to diagnose the cell damage caused by the hydrodynamic stress. In this work, we propose a novel microfluidic method to accurately assess the mechanical cell damage under a controlled extensional stress field, generated in a microfluidic cross-slot geometry. The cell damage in the extensional field is related to the oxygen bubble bursting process. We employed viscoelasticity-induced particle focusing to align the cells along the shear-free channel centerline, so that all the cells experience a similar extensional stress field, which also precludes the cell damage due to wall shear stress. We applied our novel microfluidic sensor to find the critical extensional stress to damage Chinese hamster ovary (CHO) cells; the critical stress is found to be ∼250 Pa. Our current results are relevant in the design of practical bioreactors, as our results clearly demonstrate that the control of the bubble bursting process is critical in minimizing cell damage in bioreactor applications. Further, our results will provide useful information on the biophysical cell properties under fluid flow environments.