The aim of this study was to investigate the association between incident dementia and rates of infection-related hospital contacts. We conducted a registry- and population-based matched-cohort study of all Danish residents who were born in or before 1950, included from 1 January 2000 or their 65th birthday (whichever came later), who were alive and resided in Denmark at the start of the study, excluding those who had received a dementia diagnosis before 1 January 2000 or their 65th birthday (n = 1,712,100). A total of 129,660 people (403,744 person years) with incident dementia were matched with 297,476 people (1,918,784 person years) without dementia. Incidence rate ratios (IRRs) of infection-related hospital contacts were calculated using Poisson regression, by infection type, sex and age. The IRR for any infection-related contact in dementia was 1.5, was highest for nervous and urinary system infections and sepsis, decreased with increasing age and was higher in men. More people with than without dementia had contacts five years before the index date. Our findings show that dementia is a risk factor for infection-related hospital contacts and infections might be an early sign of dementia.