BACKGROUND: SARS-CoV-2 (severe acute respiratory coronavirus 2) was spreading rapidly in South Korea at the end of February 2020 following its initial outbreak in China, making Korea the new center of global attention. The role of social media amid the current coronavirus disease (COVID-19) pandemic has often been criticized, but little systematic research has been conducted on this issue. Social media functions as a convenient source of information in pandemic situations. OBJECTIVE: Few infodemiology studies have applied network analysis in conjunction with content analysis. This study investigates information transmission networks and news-sharing behaviors regarding COVID-19 on Twitter in Korea. The real time aggregation of social media data can serve as a starting point for designing strategic messages for health campaigns and establishing an effective communication system during this outbreak. METHODS: Korean COVID-19-related Twitter data were collected on February 29, 2020. Our final sample comprised of 43,832 users and 78,233 relationships on Twitter. We generated four networks in terms of key issues regarding COVID-19 in Korea. This study comparatively investigates how COVID-19-related issues have circulated on Twitter through network analysis. Next, we classified top news channels shared via tweets. Lastly, we conducted a content analysis of news frames used in the top-shared sources. RESULTS: The network analysis suggests that the spread of information was faster in the Coronavirus network than in the other networks (Corona19, Shincheon, and Daegu). People who used the word "Coronavirus" communicated more frequently with each other. The spread of information was faster, and the diameter value was lower than for those who used other terms. Many of the news items highlighted the positive roles being played by individuals and groups, directing readers' attention to the crisis. Ethical issues such as deviant behavior among the population and an entertainment frame highlighting celebrity donations also emerged often. There was a significant difference in the use of nonportal (n=14) and portal news (n=26) sites between the four network types. The news frames used in the top sources were similar across the networks (P=.89, 95% CI 0.004-0.006). Tweets containing medically framed news articles (mean 7.571, SD 1.988) were found to be more popular than tweets that included news articles adopting nonmedical frames (mean 5.060, SD 2.904; N=40, P=.03, 95% CI 0.169-4.852). CONCLUSIONS: Most of the popular news on Twitter had nonmedical frames. Nevertheless, the spillover effect of the news articles that delivered medical information about COVID-19 was greater than that of news with nonmedical frames. Social media network analytics cannot replace the work of public health officials; however, monitoring public conversations and media news that propagates rapidly can assist public health professionals in their complex and fast-paced decision-making processes.