Background: Various surveys have documented a negative impact of the COVID-19 pandemic on the population’s mental health. There is widespread concern about a surge of suicides, but evidence supporting a link between global pandemics and suicide is very limited. Using historical data from the three major influenza pandemics of the 20th century, and recently released data from the first half of 2020, we aimed to investigate whether an association exists between influenza deaths and suicide deaths. Methods: Annual data on influenza death rates and suicide rates were extracted from the Statistical Yearbook of Sweden from 1910-1978, covering the three 20th century pandemics, and from Statistics Sweden for the period from January to June of each year during 2000-2020. COVID-19 death data were available for the first half of 2020. We implemented non-linear autoregressive distributed lag (NARDL) models to explore if there is a short-term and/or long-term effect of increases and decreases in influenza death rates on suicide rates during 1910-1978. Analyses were done separately for men and women. Descriptive analyses were used for the available 2020 data. Findings: Between 1910-1978, there was no evidence of either short-term or long-term significant associations between influenza death rates and changes in suicides. The same pattern emerged in separate analyses for men and women. Suicide rates in January-June 2020 revealed a slight decrease compared to the corresponding rates in January-June 2019 (relative decrease by −1.2% among men and −12.8% among women). Interpretation: We found no evidence of short or long-term association between influenza death rates and suicide death rates across three 20th century pandemics or during the first six months of 2020 (when the first wave of COVID-19 occurred). Concerns about a substantial increase of suicides may be exaggerated. The media should be cautious when reporting news about suicides during the current pandemic.