We propose and demonstrate the fabrication of a curved fishnet metamaterial integrated into a rolled-up tube (RUT) that consists of eight alternating layers of gold and silicon dioxide. We adopt a self-rolled technique for the fabrication of metal/dielectric microtubes with large enough diameters for optical characterization. We experimentally characterize the fabricated fishnet structure, and by means of numerical calculations, we show that the fabricated structure possesses a negative refractive index with a high figure of merit. We demonstrate that the negative refractive index region can be tuned by precisely controlling the dimensions of the holes forming the metamaterial. The results of this study open up the possibility to obtain a simple, fast, and flexible platform for the fabrication of RUT-based metamaterials for bioimaging and sensing applications.