NEW DELHI—Two weeks into the world’s biggest lockdown, India’s food supply chain is struggling with a shortage of one of its crucial commodities: people.

Essential industries—such as growing, harvesting and delivering food—are allowed to operateunder the lockdown but the people who move the essentials from farm to fork aren’t showing up for work. Stores say some basics such as eggs, yogurt and cooking oil are increasingly hard to find, a development they say could point to bigger problems ahead if things don’t return to normal in the coming month.