Luciano Sampietro lifted a three-foot aluminum pipe to his lips and blew, sending a blow dart laced with sedatives, muscle relaxers and painkillers toward the world’s largest rodent, lounging near an artificial pond.

The veterinarian’s target, a roughly 110-pound alpha male capybara, was hit in the hind leg. Mr. Sampietro fired again and struck a female. Within 15 minutes, workers dressed in the tan outfits of safari guides scooped up the sleeping patients.

But they were too late: The female was already pregnant. So they injected the male with a drug designed to stop him from impregnating any more.

Yes, in the wealthy suburbs of Buenos Aires, they are sterilizing the capybaras.

The rotund, laid-back, dog-sized rodents native to South America have recently become a darling of the modern internet. They have catapulted to the top of the unofficial adorable animal rankings via countless videos showing them mellow, plump and perfectly happy to let monkeys and ducks ride on their backs. Their image adorns backpacks and stuffed animals, and in Tokyo, tourists pay premiums to feed them carrots at capybara cafes.