Studies of single cells via microscopy and microinjection are a key component in research on gene functions, cancer, stem cells, and reproductive technology. As biomedical experiments become more complex, there is an urgent need to use robotic systems to improve cell manipulation and microinjection processes. Automation of these tasks using machine vision and visual servoing creates significant benefits for biomedical laboratories, including repeatability of experiments, higher throughput, and improved cell viability. This paper presents the development of a new 5-DOF robotic manipulator, designed for manipulating and microinjecting single cells. This biological cell manipulator (BCM) is capable of autonomous scanning of a cell culture followed by autonomous injection of cells using single-cell electroporation (SCE). SCE does not require piercing the cell membrane, thereby keeping the cell membrane fully intact. The BCM features high-precision 3-DOF translational and 2-DOF rotational motion, and a second z-axis allowing top-down placement of a micropipette tip onto the cell membrane for SCE. As a technical demonstration, the autonomous visual servoing and microinjection capabilities of the single-cell manipulator are experimentally shown using sea urchin eggs.