In a country where movie stars are treated like gods, some actors are worshiped like deities.

The 65-year-old Tamil actor Shivaji Rao Gaekwad, better known as Rajinikanth, is one of India’s most celebrated and well-paid movie stars. For decades, fans have regularly bathed pictures of him in thousands of gallons of milk, a sign of devotion usually reserved for Hindu idols.

With every new film Rajinikanth releases, milk becomes so much in demand in some parts of the country that it is stolen from markets, resulting in shortages that potentially endanger malnourished children, officials and activists say.

Die-hard fans can pour about 11,000 to 16,000 gallons of milk a day over billboards and cardboard cutouts of Rajinikanth in the weeks after a new release, said S. A. Ponnusamy, president of the Tamil Nadu Milk Dealers Employees Welfare Association, who opposes the practice. Mr. Ponnusamy said some fans had resorted to stealing milk before daybreak when dairy workers drop it off outside shops.

Last month, before the release of Rajinikanth’s latest film, “Kabali,” a box office record breaker, the milk dealers’ association asked the actor to “sternly admonish” his loyal fans for wasting milk, and it encouraged him instead to organize blood and organ donation drives outside movie theaters.