The Sustainable Development Goals (SDGs) are increasingly being used to measure developmental progress among and within countries. Achieving the health-related SDGs remains a primary concern of many developing countries. This study measured the progress in selected health-related indicators of SDGs in the states of India by social and economic groups, and predicted their likely progress by 2030. The health indicators analysed included health outcomes, nutrition, health care utilization and determinants of health. Data from the Census of India, Sample Registration System (SRS), National Family and Health Surveys (NFHSs) and National Sample Survey Organization (NSSO) were used in the analysis. Annual rate of progress (ARP) and the required rate of progress (RRP) were computed for selected indicators over the period 2005–06 to 2015–16. A Composite Index of Health (CIH) was used to understand the state of health of populations. The ARP was higher than the RRP in maternal care and reduction of under-five mortality, while ARP was lower than the RRP in undernutrition and sanitation. The ARP for health-related indicators showed a mixed pattern across religion and caste groups. The ARP for medical assistance at birth and immunization was highest among Scheduled Castes and that for reduction of under-five mortality was highest among Scheduled Tribes. The CIH was lowest in Uttar Pradesh (0.26) and highest in Goa (0.81). The association between the CIH and the Human Development Index (HDI) was significant, suggesting interlinkage between health and development. Notable improvements were observed in maternal and child health and maternal health care utilization across social groups in India over the period 2005–06 to 2015–16, and if the trends continue the country can achieve the SDG target in maternal health by 2030. However, progress in nutrition and other health indicators has been slow and uneven.