Oxide heterostructures represent a unique playground for triggering the emergence of novel electronic states and for implementing new device concepts. The discovery of 2D conductivity at the interface has been linking for over a decade two of the major current research fields in Materials Science: correlated transition-metal-oxide systems and low-dimensional systems. A full merging of these two fields requires nevertheless the realization of heterostructures in the form of freestanding membranes. Here we show a completely new method for obtaining oxide hetero-membranes with micrometer lateral dimensions. Unlike traditional thin-film-based techniques developed for semiconductors and recently extended to oxides, the concept we demonstrate does not rely on any sacrificial layer and is based instead on pure strain engineering. We monitor through both real-time and post-deposition analyses, performed at different stages of growth, the strain relaxation mechanism leading to the spontaneous formation of curved hetero-membranes. Detailed transmission electron microscopy investigations show that the membranes are fully epitaxial and that their curvature results in a huge strain gradient, each of the layers showing a mixed compressive/tensile strain state. Electronic devices are fabricated by realizing ad hoc circuits for individual micro-membranes transferred on silicon chips. Our samples exhibit metallic conductivity and electrostatic field effect similar to 2D-electron systems in bulk heterostructures. Our results open a new path for adding oxide functionality into semiconductor electronics, potentially allowing for …