Ionic liquids (ILs) form a variety of nanostructures due to their amphiphilic nature. Recently, unusual structural phenomena have been found in glassy ILs near their glass transition temperatures; however, in all studied cases, IL cations and anions were in the form of separate moieties. In this work, we investigate for the first time such structural anomalies in zwitterionic IL glasses (ZILs), where the cation and anion are bound in a single molecule. Such binding reasonably restricts mutual diffusion of cations and anions, leading to modification of nano-ordering and character of structural anomalies in these glassy nanomaterials, as has been investigated using Electron Paramagnetic Resonance (EPR) spectroscopy. In particular, the occurrence of structural anomalies in ZIL glasses was revealed, and their characteristic temperatures were found to be higher compared to common ILs of a similar structure. Altogether, this work broadens the scope of structural anomalies in ionic liquid glasses and indicates new routes to tune their properties.