We use micropatterning and strain engineering to encapsulate single living mammalian cells into transparent tubular architectures consisting of three-dimensional (3D) rolled-up nanomembranes. By using optical microscopy, we demonstrate that these structures are suitable for the scrutiny of cellular dynamics within confined 3D-microenvironments. We show that spatial confinement of mitotic mammalian cells inside tubular architectures can perturb metaphase plate formation, delay mitotic progression, and cause chromosomal instability in both a transformed and nontransformed human cell line. These findings could provide important clues into how spatial constraints dictate cellular behavior and function.