During the 2019 novel coronavirus disease (COVID-19) pandemic in 2020, limited data from several countries suggested reduced circulation of seasonal influenza viruses. We applied the moving epidemic method (MEM) to influenza surveillance data from 2016 to 2019 in Bangladesh to estimate an average seasonal influenza curve and establish epidemic thresholds. The 2020 influenza epidemic started 18 weeks later, was 7.5 weeks shorter, and was less intense than the average curve of the four previous years. These findings contribute to a limited but growing body of evidence that influenza seasons were altered globally in 2020.