Abstract Background Patients with psoriasis have a high risk for multiple comorbid conditions. However, few studies have examined the association between psoriasis and severe and rare infections. This study reports the incidence of severe and rare infections (considered as rare in Denmark) among Danish patients with psoriasis, compared with the general population. Objectives The objectives of this study were to assess the incidence and risk of severe and rare infections in Danish patients with psoriasis and the matched general population, and to compare this risk for patients with severe or mild psoriasis with that of the general population. Methods Data for individuals aged ≥18 years who were alive and resident in the source population were collected from the Danish National Patient Register between 1 January 1997 and 31 December 2018. Individuals with any of the investigated chronic infections prior to inclusion were excluded. Patients with psoriasis were matched (1 : 6) for age and sex with general population controls. Severe infections were defined as infections requiring treatment in a hospital setting and rare infections included HIV, hepatitis B and C, and tuberculosis infections. Incidence rates (IRs) were reported per 100 000 person-years of exposure. Severe psoriasis was defined according to previous or active use of systemic or biological treatment. Patients who never received biological and/or systemic treatment were categorized as having mild psoriasis. Results A total of 94 450 patients with psoriasis were matched with 566 700 controls. The respective IRs were higher for patients with any psoriasis compared with controls; IR 3104·9 [95% confidence interval (CI) 3066·6 to 3143·7] and IR 2381·1 (95% CI 2367·6 to 2394·6) for any infection, IR 3080·6 (95% CI 3042·5 to 3119·3) and IR 2364·4 (95% CI 2350·9 to 2377·9) for severe infections, and IR 42·9 (95% CI 38·89 to 47·4) and IR 31·8 (95% CI 30·34 to 33·3) for rare infections, respectively. Patients with severe psoriasis had higher IRs of severe or rare infections (IR 3847·7, 95% CI 3754·3 to 3943·4) compared with patients with mild psoriasis and controls. Conclusions As the severity of psoriasis increases, so does the risk of severe and rare infections. Therefore, clinicians should be aware of the increased risk of severe and rare infections in patients with severe psoriasis so that early investigation and treatment can be initiated. What is already known about this topic? Few studies have looked at the incidence and prevalence of serious infections (associated with hospitalization) and rare infections including tuberculosis, hepatitis B and C, and HIV among patients with different severities of psoriasis. What does this study add? Patients with psoriasis have an increased risk of severe and rare infections. Clinicians should be aware of the increased risk of severe and rare infections in patients with severe psoriasis so that early investigation and treatment can be initiated.