Mr. Ferretti, 36 years old, and Mr. Lopez, 44, had enjoyed themselves under the supervision of a doctor for what some are calling a brosectomy—a vasectomy with friends in a cushy setting of couches, snacks, big-screen TV, and in some clinics, top-shelf liquor.

The University of Utah Health in Salt Lake City has run March Madness promotions for the past three years. It offers a vasectomy package that includes a Utah Jazz basketball ticket giveaway, goody bags and basketball-shaped ice packs. This year, its surgeons performed more than three times as many vasectomies in March compared with the average number done in the other months through May, according to the health center’s internal marketing data.