Cell morphology plays an important role in maintaining normal cellular functions. Existing techniques for cell morphology measurement, such as confocal imaging and atomic force microscopy, have the limitations of photobleaching and incompatibility for integration with other cell manipulation instruments. This paper reports a robotic cell manipulation system that is capable of measuring changes of cell morphologies. This capability is enabled by several key techniques including cell recognition, determination of contact points on a cell, and two vision-based contact detection methods for measuring cell bottom and top surface positions. With the detected cell contour and height information, three-dimensional cell morphology is reconstructed. Experiments show that the cell morphology measurement technique has an overall success rate of 95.67%, an average measurement speed of 2.63 s/contact, and a measurement error of 4.65%. The cell morphology measurement results indicate that bladder cancer cells with higher metastatic potential exhibit lower cell heights than earlier-stage cancer cells because of more disorganized cytoskeleton networks. We also applied the robotic system to microinject the drug Cytochalasin D into cancer cells, and the drug effect on cell morphology changes was quantified.