Since its outbreak, the SARS-CoV-2 pandemic has shown complex dynamics in both time and space. These dynamics are the result of a combination of factors, including the spatial distribution of the population’s social and economic levels and its mobility patterns within a given country. After assessing the risk of infection and associated uncertainty based on infection rates by municipality, one of the most important challenges now facing health authorities concerns the ability to predict second waves and interactions with epidemics of other viruses (e.g. influenza). We propose characterizing the local spatiotemporal behaviour of risk of infection based on existing historical data, and classifying the local spatiotemporal patterns of the time series, thus allowing the management of new waves by region. We combined functional data analysis with geostatistical simulation to model the spatiotemporal evolution of infection risk by COVID-19 in mainland Portugal. The daily number of infection data by municipality reported by the Portuguese Directorate-General for Health are used to build time series of infection since the beginning of the outbreak in Portugal. We employ a dimensionality reduction of these curves using functional principal component analysis. The objective of this step is twofold: detect municipalities with a similar temporal evolution, and get a small number of coefficients to describe the temporal pattern of the series. The low-dimension coefficients are then used as experimental data to map the infection time series spatially using geostatistical simulation. With this step, we recover high-resolution maps of COVID-19 infection risk at any time step, allowing the simultaneous modelling of time and space. With the resulting spatiotemporal models, authorities can identify locations where the disease exhibits similar behaviours and, therefore, devise mitigation actions based on previous experience. Also, the models may be used for short-term forecasting as a simple data-driven proxy of full SEIR (susceptible, exposed, infectious, recovered) models.