Abnormal cell mechanical stiffness can point to the development of various diseases including cancers and infections. We report a new microfluidic technique for continuous cell separation utilizing variation in cell stiffness. We use a microfluidic channel decorated by periodic diagonal ridges that compress the flowing cells in rapid succession. The compression in combination with secondary flows in the ridged microfluidic channel translates each cell perpendicular to the channel axis in proportion to its stiffness. We demonstrate the physical principle of the cell sorting mechanism and show that our microfluidic approach can be effectively used to separate a variety of cell types which are similar in size but of different stiffnesses, spanning a range from 210 Pa to 23 kPa. Atomic force microscopy is used to directly measure the stiffness of the separated cells and we found that the trajectories in the microchannel correlated to stiffness. We have demonstrated that the current processing throughput is 250 cells per second. This microfluidic separation technique opens new ways for conducting rapid and low-cost cell analysis and disease diagnostics through biophysical markers.