Predicting the short-term evolution of the number of cancers is essential for planning investments and allocating health resources. The objective of this study was to predict the numbers of cancer cases and of the 12 most frequent cancer sites, and their age-standardized incidence rates, for the years 2019–2025 in Switzerland. Projections of the number of malignant cancer cases were obtained by combining data from two sources: forecasts of national age-standardized cancer incidence rates and population projections from the Swiss Federal Statistical Office. Age-standardized cancer incidence rates, approximating the individual cancer risk, were predicted by a low-order Autoregressive Integrated Moving Average (ARIMA) model. The contributions of changes in cancer risk (epidemiological component) and population aging and growth (demographic components) to the projected number of new cancer cases were each quantified. Between 2018 and 2025, age-standardized cancer incidence rates are predicted to stabilize for men and women at around 426 and 328/100,000, respectively (<1% change). These projected trends are expected for most cancer sites. The annual number of cancers is expected to increase from 45,676 to 52,552 (+15%), more so for men (+18%) than for women (+11%). These increases are almost entirely due to projected changes in population age structure (+12% for men and +6% for women) and population growth (+6% for both sexes). The rise in numbers of expected cancers for each site is forecast to range from 4.15% (thyroid in men) to 26% (bladder in men). While ranking of the three most frequent cancers will remain unchanged for men (1 ^st prostate, 2 ^nd lung, 3 ^rd colon-rectum), colorectal cancer will overtake by 2025 lung cancer as the second most common female cancer in Switzerland, behind breast cancer. Effective and sustained prevention measures, as well as infrastructural interventions, are required to counter the increase in cancer cases and prevent any potential shortage of professionals in cancer care delivery.