Quantum Technologies (QT), and their use in space applications, are potentially transformative innovations with fundamental implications for society and the global economy. A new era of QT is emerging in the space domain, with a range of space missions already carrying quantum cryptography payloads. Both the quantum and space domains have evolved as strategically important technology sectors that address some of the major challenges of the modern digital era, and now they are being used inter-operatively. The paper analyses the intersections between these two sectors. It highlights legal and regulatory issues to be considered at this relatively early stage of ‘quantum technology for space’, in particular cybersecurity, data transfer protection and liability. As quantum cryptography becomes increasingly important, it is necessary to assess the extent to which those quantum systems utilised in space missions will comply with applicable cybersecurity regulations, current encryption standards, as well as data transfer and protection regulations. The paper also examines the applicability of the UN Space Treaties.