Herpes zoster can cause rare but serious complications; the frequency of these complications has not been well described. To quantify the risks of acute non-postherpetic neuralgia (PHN) zoster complications, to inform vaccination policy. We conducted a cohort study among unvaccinated immunocompetent adults with incident zoster, and age-, sex- and practice-matched control adults without zoster, using routinely collected health data from the UK Clinical Practice Research Datalink (years 2001 to 2018). Crude attributable risks of complications were estimated as the difference between Kaplan-Meier-estimated 3-month cumulative incidences in patients with zoster vs. controls. We used Cox models to obtain hazard ratios for our primary outcomes in patients with and without zoster. Primary outcomes were ocular, neurological, cutaneous, visceral and zoster-specific complications. We also assessed whether antivirals during acute zoster protected against the complications. In total 178 964 incident cases of zoster and 1 799 380 controls were included. The absolute risks of zoster-specific complications within 3 months of zoster diagnosis were 0·37% [95% confidence interval (CI) 0·34-0·39] for Ramsay Hunt syndrome, 0·01% (95% CI 0·0-0·01) for disseminated zoster, 0·04% (95% CI 0·03-0·05) for zoster death and 0·97% (95% CI 0·92-1·00) for zoster hospitalization. For other complications, attributable risks were 0·48% (95% CI 0·44-0·51) for neurological complications, 1·33% (95% CI 1·28-1·39) for ocular complications, 0·29% (95% CI 0·26-0·32) for cutaneous complications and 0·78% (95% CI 0·73-0·84) for visceral complications. Attributable risks were higher among patients > 50 years old. Patients with zoster had raised risks of all primary outcomes relative to controls. Antiviral prescription was associated with reduced risk of neurological complications (hazard ratio 0·61, 95% CI 0·53-0·70). Non-PHN complications of zoster were relatively common, which may affect cost-effectiveness calculations for zoster vaccination. Clinicians should be aware that zoster can lead to various complications, besides PHN.