Background: Hospital health care workers are at high risk of developing COVID-19 and transmitting the disease to their family upon returning home; the aim here is to estimate the secondary attack rate of COVID-19 in household contacts of health care workers and their transmission risk factors. Material and Methods: COVID-19 cases in the health care workers of an academic hospital in Pamplona, Spain, from 2 March to 26 May 2020, were followed up. The secondary attack rate (SAR) was estimated from cases in household contacts of index cases and their risk factors by Poisson regression. Results: 89 index cases were studied from 99 notified cases in health care workers (89.0%), excluding secondary cases or those who lived alone. Forty-six secondary cases confirmed by the laboratory were found among 326 household contacts, a secondary attack rate of 14.11% (95% CI 10.75–18.31), and 33 household contacts with acute infection symptoms without microbiologic confirmation 10.12% (95% CI 7.30–13.87). Considering all the cases, the secondary attack rate was 27.3 (95% CI 22.75–32.38). Risk factors were the gender and profession of the index case, the number of people living in the household, and the number of persons per bedroom. When the index case health worker used a single room, it had a protective effect, with an incidence rate ratio (IRR) of 0.493 (95% CI 0.246–0.985); Conclusions: The secondary attack rate found among household contacts of health care workers is high. The preventive isolation of health care workers in individual rooms in their house may reduce the transmission in their families.