The coronavirus disease 2019 (COVID-19) pandemic has led to capacity problems in many hospitals around the world. During the peak of new infections in Germany in April 2020 and October to December 2020, most hospitals had to cancel elective procedures for patients because of capacity shortages. We present a scalable forecasting framework with a Monte Carlo simulation to forecast the short-term bed occupancy of patients with confirmed and suspected COVID-19 in intensive care units and regular wards. We apply the simulation to different granularity and geographical levels. Our forecasts were a central part of the official weekly reports of the Bavarian State Ministry of Health and Care, which were sent to key decision makers in the individual ambulance districts from May 2020 to March 2021. Our evaluation shows that the forecasting framework delivers accurate forecasts despite data availability and quality issues.