While there has been recent success in audio-based COVID-19 detection, challenges still exist in developing more reliable and generalised models due to the limited amount of high quality labelled audio recordings. With a substantial amount of unlabelled audio recordings available, exploring semi-supervised learning (SSL) may benefit COVID-19 detection by incorporating this extra data. In this paper, we propose a SSL framework which adjusted FixMatch, one of the most advanced SSL approaches, to audio signals and explored its effectiveness in COVID-19 detection. The proposed framework is validated with a crowd-sourced audio database collected from our app, and showed superior performance over supervised models with a maximum of 7.2\% relative improvement. Furthermore, we demonstrated that the proposed framework significantly benefits model development using imbalanced datasets, which is a common challenge in clinical data. It can also improve model generalisation. This potentially paves a new pathway of utilising unlabelled data effectively to build more accurate and reliable COVID-19 detection tools.