Health organizations have widely adopted social media for health promotion, public health communication conveyance, and organizational promotion activities. However, little published data exists on the factors that facilitate health information diffusion in South East Asia, especially Malaysia compared with Western countries. This study aimed to investigate factors associated with good engagement rates among internet users on the Facebook (FB) page of Ministry of Health Malaysia. In this observational study, 2123 FB posts were randomly selected. Data dated from 1 November 2016 to 31 October 2017 was gathered from the Facebook Insight. The logistic regression model was applied to identify factors associated with good engagement rates. This study found that a FB post with a good engagement rate was significantly associated with a health education post (Adjusted Odd Ratio (AOR): 3.80, 95% Confidence Interval CI: 3.02–4.78, p < 0.001), a risk communication post (AOR: 1.77, 95% CI: 1.39–2.26, p < 0.001), a post in the afternoon (AOR: 1.76, 95% CI: 1.34–2.31, p < 0.001) or in the evening (AOR: 1.48, 95% CI: 1.20–1.82, p < 0.001), and a video format (AOR: 3.74, 95% CI: 1.44–9.71, p = 0.007). Therefore, we present the first comprehensive analysis of health information engagement among internet users in Malaysia. The growing trends of online health information-seeking behaviors and demand for the availability of validated health information require effective strategies by public health organizations to disseminate health information and achieve better audience engagement on social media.