In July 2022, the World Health Organization (WHO) declared the rapidly spreading monkeypox outbreak a global health emergency; in the future, this may cause the closure of higher education institutions and a shift toward digital learning. As before, specifically in March 2020, the WHO expressed that COVID-19 is a worldwide pandemic. This transformation was accompanied by the widespread adoption of mobiles and their applications in learning with organised or non-organised forms. Although many articles have recorded the importance and effectiveness of mobile learning in higher education, other articles have indicated the weak utilisation of mobile learning amid the COVID-19 pandemic, especially by university educators (UEs). In addition, these articles often focus on the opportunities, challenges, and weaknesses of mobile learning amid COVID-19, but few studies have handled the acceptance of the UEs to adopt a mobile learning approach amid COVID-19 by the unified theory of acceptance and use of technology (UTAUT). This article’s main contribution is extending the (UTAUT) model in context and reviewing the acceptance of the adoption of mobiles and their applications in education as an approach amid global health emergencies, i.e., COVID-19 and monkeypox. The data were gathered from university educators (N = 392) in Saudi Arabia. The hypotheses were evaluated with data that were analysed using structural equation modelling (SEM). The results demonstrated that six of the eight hypotheses had high and significant effects on behaviour intention (performance expectancy (PE), effort expectancy (EF), social influence (SI), facilitating conditions (FC), self-efficacy (SE), and users’ awareness (UA)). Two of the eight factors have insignificant or negative impacts on behaviour intention (users’ perceptions (UP) and technology challenges (TC)), which need an additional review by policymakers, practitioners, mobile learning providers, and investigators looking to develop efficient strategies concerning mobile learning.