The properties and structures of viruses are directly related to the three‐dimensional structure of their capsid proteins, which arises from a combination of hydrophobic and supramolecular interactions, such as hydrogen bonds. The design of synthetic materials demonstrating similar synergistic interactions still remains a challenge. Herein, we report the synthesis of a polymer/cyclic peptide conjugate that combines the capability to form supramolecular nanotubes via hydrogen bonds with the properties of an amphiphilic block copolymer. The analysis of aqueous solutions by scattering and imaging techniques revealed a barrel‐shaped alignment of single peptide nanotubes into a large tubisome (length: 260 nm (from SANS)) with a hydrophobic core (diameter: 16 nm) and a hydrophilic shell. These systems, which have a structure that is similar to those of viruses, were tested in vitro to elucidate their activity on cells. Remarkably, the rigid tubisomes are able to perforate the lysosomal membrane in cells and release a small molecule into the cytosol. Peptides and polymers: Polymer/cyclic peptide conjugates form supramolecular tubisome structures with a hydrophobic core and a hydrophilic shell. They perforate the lysosomal membrane in cells to release a small molecule into the cytosol.