While having social support can contribute to better health, those in poor health may be limited in their capacity to receive social support. We studied the health factors associated with social support among community-dwelling older adults in Singapore. We used data from the third follow-up interviews (2014–2016) of 16,943 participants of the Singapore Chinese Health Study, a population-based cohort of older Singapore Chinese. Participants were interviewed at a mean age of 73 years (range 61–96 years) using the Duke Social Support Scale (DUSOCS). We first applied ordinary least squares regression to DUSOCS scores and found that those with instrumental limitations, poor self-rated health, cognitive impairment and depression had lower social support scores. We then applied latent class analysis to DUSOCS answer patterns and revealed four groups of older adults based on the source and amount of social support. Among them, compared to the ‘overall supported’ group (17%) with the highest social support scores and broad support from family members and non-family individuals, the ‘family restricted’ (50%) group had the lowest social support scores and only received support from children. Health factors associated with being ‘family restricted’ were instrumental limitations (odds ratio (OR) = 1.33, 95% confidence interval (CI) = 1.19–1.49), poor self-rated health (OR = 1.40, 95% CI = 1.28–1.53), cognitive impairment (OR = 1.19, 95% CI = 1.04–1.37) and depression (OR = 2.50, 95% CI = 2.22–2.82). We found that while older adults in poor health have lower social support scores, they were more likely to receive a lot of support from children. Our results showed that lower social support scores among Singaporean older adults in poor health may not indicate lack of social support, but rather that social support is restricted in scope and intensified around children. These results may apply to other Asian societies where family plays a central role in elder-care.