Background: Janus kinase inhibitors (JAKi), tumor necrosis factor inhibitors (TNFi), and interleukin-6 receptor inhibitors (IL-6i) are widely used for rheumatoid arthritis (RA). Infection risks across targeted therapies in Asian patients remain unclear. Methods: Using Korean National Health Insurance Service claims data (2014–2023), we conducted a new-user cohort study of adults with RA. Three pairwise comparisons (JAKi vs TNFi, JAKi vs IL-6i, and IL-6i vs TNFi) were constructed using 1:1 propensity score matching. Hazard ratios (HRs) for overall infection, herpes zoster (HZ), serious HZ, opportunistic infection (OI), and serious bacterial infection (SBI) were estimated under intention-to-treat and on-treatment frameworks. Results: JAKi were associated with higher HZ risk than TNFi (on-treatment HR 2.42; 95% confidence interval [CI] 2.06–2.83) and IL-6i (HR 2.60; 95% CI 2.06–3.28); IL-6i and TNFi did not differ (HR 0.99; 95% CI 0.79–1.25). Overall infection and serious HZ risks were also higher with JAKi. OI risk did not differ across classes. IL-6i were associated with higher SBI risk than TNFi (HR 1.64; 95% CI 1.28–2.11). Conclusions: Elevated HZ risk appeared specific to JAKi, while IL-6i and TNFi had comparable HZ risks. Higher SBI risk with IL-6i than TNFi indicates that infection risks vary by drug class and infection type. HZ prevention and monitoring are particularly important with JAKi.