The COVID-19 pandemic has harmed the global tourism and hospitality industry, crippling foreign currency earnings and employment in many countries, South Africa (SA) included. This study aims to evaluate the impact of the COVID-19 pandemic on overseas tourist arrivals to SA, and to make an inference on the country’s foreign currency earnings on economic development. The Box–Jenkins methodology is used in fitting non-seasonal integrated autoregressive moving average (ARIMA) and seasonal ARIMA (SARIMA) models to quantify and characterise the number of overseas tourists to SA. The ARIMA 1,0,1(0,1,1)12 model is the best fitting model for the overseas tourist arrivals data to SA, as confirmed by the Akaike Information Criterion (AIC). The model shows good forecasting power in the absence of the COVID-19 pandemic, as evidenced by the validation results. The difference between forecasts and actual values after the validation phase shows the negative impact of the COVID-19 pandemic on overseas tourist arrivals to SA and the challenges it poses to the statistical modelling of tourist arrivals to SA, considering the pandemic was the first of its kind. The COVID-19 pandemic exposed the tourism industry’s vulnerability to economic shocks, showing the need for aggressive marketing strategies that may revamp the tourism sectors to levels previously expected before and or after COVID-19 for sustainable development.