When a doctor in southeastern Pakistan sounded alarm bells in April about children mysteriously testing positive for HIV, health officials decided to offer screening to his entire town. What they found, the World Health Organization said, was unprecedented.

Over six weeks of testing, more than 600 children in the town, most of them between 2 and 5 years old, tested positive for the virus that causes AIDS, while nearly all their parents tested negative. Authorities have begun screening people in nearby towns, and the number...