“We’ll never have enough to satisfy demand,” Mr. Melnitsky said.

Indeed, the new model may represent a prime arbitrage opportunity for anyone fortunate enough to get hold of one but crazy enough to sell it. “I wouldn’t be surprised to see these new Daytona models get flipped in the secondary market for a cool $5,000 premium over retail in the first six months,” said Paul Altieri, who runs Bob’s Watches, a prominent online dealer of vintage Rolexes in Westminster, Calif. “I could sell 10 of them tomorrow.”

This is hardly the first time that the Rolex Daytona has created a fuss. The storied chronograph, named after the Daytona speedway in Florida, debuted in the 1960s as a tool for auto racing enthusiasts. With its three subdials for timing laps, it was basically the world’s most regal stopwatch.

By the 1970s, it was already achieving icon status, with a big boost from Paul Newman, who adopted it as his signature timepiece when he developed a passion for motor sports.

In the years since, the Daytona has become the rare timepiece coveted by both tweedy collectors (Christie’s sold a so-called Paul Newman model from 1969 for $1.1 million in 2013) and paparazzi-dodging celebrities (Daniel Craig, Adam Levine and Eric Clapton, to name a few).

Anticipation of the new model has been building for years, especially after Rolex redesigned its Submariner and GMT-Master II models with Cerachrom, a scuff- and fade-resistant ceramic that infuses these venerable midcentury models with a 21st-century flair.

The wait was finally over in March. “My phone started vibrating nonstop at Baselworld moments after Rolex raised the green window shades,” said Stephen Pulvirent, a watch journalist and editor at Surface magazine. “Everybody was chirping, ‘It’s finally here.’”

That same day, some even lined up outside the Fifth Avenue flagship of Wempe Jewelers, a prominent Rolex dealer, before it opened, said Ruediger Albers, the president of American Wempe Corporation.