The incubation period, or the time from infection to symptom onset, of COVID-19 has usually been estimated by using data collected through interviews with cases and their contacts. However, this estimation is influenced by uncertainty in the cases' recall of exposure time. We propose a novel method that uses viral load data collected over time since hospitalization, hindcasting the timing of infection with a mathematical model for viral dynamics. As an example, we used reported data on viral load for 30 hospitalized patients from multiple countries (Singapore, China, Germany, and Korea) and estimated the incubation period. The median, 2.5, and 97.5 percentiles of the incubation period were 5.85 days (95 % CI: 5.05, 6.77), 2.65 days (2.04, 3.41), and 12.99 days (9.98, 16.79), respectively, which are comparable to the values estimated in previous studies. Using viral load to estimate the incubation period might be a useful approach, especially when it is impractical to directly observe the infection event.