Biological cell injection is an effective method in which a foreign material is directly introduced into a biological cell. Since human involvement reduces the success rate of the biological microinjection procedure, an extensive research effort has been made towards its automation. The accurate positioning of a randomly placed biological cell in the microscope's field of view is a prerequisite for any automated injection procedure. Vision is the primary source for visual servoing in microinjection applications. For this reason, a visual sensing system is required to recognise, calculate, and manipulate the cell to the desired position. In this study, eight different pretrained neural networks were analysed and used as a backbone for the YOLOv2 object detection method, and the optimal network was evaluated based on mean Intersection over Union (IoU) accuracy, average precision (AP) at different thresholds, and frame rate (fps) in our dataset. YOLOv2 with Resnet-50 model demonstrated superior performance with 89% mean IoU accuracy and 100% detection accuracy at an average of 33 fps. Ten different sets of experiments were conducted to examine the algorithm by verifying the zebrafish embryo gradual presence within the field of view to bring the zebrafish embryo to the predefined position. Experimental results demonstrated that the developed solution performed real-time with high accuracy and illustrates auto-positioning with a 100% success rate regardless of the initial position of the biological cell within the Petri dish. Later, the generalization of the proposed solution was verified in a different dataset from the real microinjection setup.