Automated robotic bio-micromanipulation can improve the throughput and efficiency of single-cell experiments. Adherent cells, such as fibroblasts, include a wide range of mammalian cells and are usually very thin with highly irregular morphologies. Automated micromanipulation of these cells is a beneficial yet challenging task, where the machine vision sub-task is addressed in this article. The necessary but neglected problem of localizing injection sites on the nucleus and the cytoplasm is defined and a novel two-stage model-based algorithm is proposed. In Stage I, the gradient information associated with the nucleic regions is extracted and used in a mathematical morphology clustering framework to roughly localize the nucleus. Next, this preliminary segmentation information is used to estimate an ellipsoidal model for the nucleic region, which is then used as an attention window in a k-means clustering-based iterative search algorithm for fine localization of the nucleus and nucleic injection site (NIS). In Stage II, a geometrical model is built on each localized nucleus and employed in a new texture-based region-growing technique called Growing Circles Algorithm to localize the cytoplasmic injection site (CIS). The proposed algorithm has been tested on 405 images containing more than 1,000 NIH/3T3 fibroblast cells, and yielded the precision rates of 0.918, 0.943, and 0.866 for the NIS, CIS, and combined NIS-CIS localizations, respectively.