Tracking cells and detecting mitotic events in time-lapse microscopy image sequences is a crucial task in biomedical research. However, it remains highly challenging due to dividing objects, low signal-to-noise ratios, indistinct boundaries, dense clusters, and the visually similar appearance of individual cells. Existing deep learning-based methods rely on manually labeled datasets for training, which is both costly and time-consuming. Moreover, their generalizability to unseen datasets remains limited due to the vast diversity of microscopy data. To overcome these limitations, we propose a zero-shot cell tracking framework by integrating Segment Anything 2 (SAM2), a large foundation model designed for general image and video segmentation, into the tracking pipeline. As a fully-unsupervised approach, our method does not depend on or inherit biases from any specific training dataset, allowing it to generalize across diverse microscopy datasets without fine-tuning. Our approach achieves competitive accuracy in both 2D and large-scale 3D time-lapse microscopy videos while eliminating the need for dataset-specific adaptation. The source code is publicly available at https://github.com/zhuchen96/sam4celltracking .