This study investigates the relationship between foreign direct investment (FDI) and health indicators—life expectancy (LE) and infant mortality rate—using both linear and non-linear Granger causality tests. Our findings reveal that there exist significant bidirectional causality between FDI and health metrics in India and China. Improvements in health metrics attract FDI, while an increase in FDI positively influences life expectancy. In contrast, Brazil and South Africa exhibit unidirectional causality from FDI to LE in the linear framework but bidirectional causality in the non-linear model, indicating the presence of complex interdependencies. However, for the Russian Federation, no significant causal relationship is observed, implying that FDI and health metrics do not influence each other in a linear or non-linear sense. To further explore these dynamics, we develop a three-sector general equilibrium model where two sectors produce final traded goods, and a third non-traded sector provides health services. Our model demonstrates that transitioning from a regime of international health capital immobility to mobility can lead to the expansion of the health sector. In a variant of the model, we show that health sector output increases under international health capital mobility. However, under full international capital mobility, one sector—either Agriculture or Manufacturing—may contract and ultimately vanish. These findings provide a theoretical foundation for understanding the impact of trade and FDI on the health sector and its sectoral implications for developing economies. Our results highlight the necessity of strategic policy frameworks to balance trade, health investment, and sectoral development.