This paper presents the design and development of a new microinjection system with force sensing for automated multi-cell injection in genome editing of zebrafish using the CRISPR/Cas9 system. In comparison with the traditional approach, it achieves a high injection speed and high precision of operation, which leads to consistent quality and high survival rate of the injected cells. One unique feature is that force sensing is employed to determine the exact moment when the cell membrane is pierced, which contributes to the protection of the cell from damage. Moreover, a new cell holding device is designed to immobilize the cells, which speeds up the multi-cell microinjection process by eliminating the use of conventional vacuum holding pipette. The system implements the object detection by machine vision algorithm along with position/force regulation. The machine vision is realized by combining the pyramid template matching algorithm with Kalman filter, which reduces the computation time and facilitates real-time control. The experimental studies are conducted to verify the performance of the developed system. Results demonstrate the reliability of the robotic microinjection system, which offers a more consistent injection quality and higher viability of cells over the skilled human operator.