The COVID-19 pandemic has increased the importance of health literacy in disseminating information on health in a non-contact society. This study focused on examining the acceptance capacity by older adults of smart devices in Korea and investigating the potential differences between men and women in terms of e-health literacy and technology-use anxiety. The study included 1369 respondents who were adults over 50 years of age and used welfare centers, public health centers, senior citizen centers, and exercise centers in Seoul and Incheon. An online survey was conducted from 1 June 2021 to 24 June 2021. The study found that the older adults’ low levels of digital literacy could limit their access to health information and negatively impact their health. The difference between men and women in terms of technology-use anxiety was statistically significant, with the latent mean for men being higher than that for women. The effect sizes of the potential mean differences were found to be at a medium level for e-health literacy and a significant level for technology-use anxiety. With Korea’s aging population and the need for the continuous management of chronic diseases among older adults, it is essential to discuss internet-based health information for disease maintenance and treatment.