Zinc oxide is a novel material system for mid-infrared and THz optoelectronics. Especially its non-polar m-plane orientation is a promising candidate for the design of devices like quantum cascade lasers (QCLs) and detectors (QCDs). But for their realization novel fabrication schemes are needed. We present a new inductively coupled plasma reactive ion etching (ICP-RIE) process for etching of m-Zn(Mg)O heterostructures in a CH4-based chemistry. The process has been optimized for smooth vertical sidewalls together with high selectivity towards a SiN etch mask. This was achieved by combining the RIE etching with wet chemical etching in strongly diluted HCl. Similar to various types of semiconductor-based optoelectronic materials and devices (Sidor et al 2016 J. Electron. Mater. 45 4663–7; Ma et al 2016 Opt. Express 24 7823), including other wide-gap semiconductors like (In)GaN (Zhang et al 2015 Nanotechnology 26), we observe surface leakage currents in etched m-plane Zn(Mg)O structures. We show that they depend on the applied etching process and surface treatment techniques as well as the barrier composition in the Zn(Mg)O heterostructures. In addition, a treatment in hydrogen peroxide (H2O2) yields a significant surface leakage current suppression up to several orders of magnitude.