Ms. Putnam, 35, does Google those who have bought the Mirror, just as she used to with first-time clients at Refine Method, the eight-year-old boutique gym she founded. But often she only finds out whom the purchase is for when the company arrives at the customer’s home to install it, or when her company receives questions about putting the device on a very high-security Wi-Fi network.

“That’s how we found out about Leslie Mann and Judd Apatow,” Ms. Putnam said, referring to the firewall issue. Her company, whose offices are in the NoMad neighborhood of New York and has raised $38 million in funding from investors including Spark Capital (Foursquare, Warby Parker) and First Round Capital (Uber, Blue Apron), is selling $1 million of the 1.4-inch-thick Mirrors per month, she said.

There are buyers in all 50 states, with California, perhaps not surprisingly, the top market. Luxury hotels have begun installing Mirrors in suites and, in the case of the Mark, its $75,000-per-night penthouse. (Not all customers are 1-percenters, Ms. Putnam stressed; roughly 20 percent request financing.)

Ms. Putnam is refreshingly new to the courting of celebrity, and speaks of influencers (she gave Mirrors to Sara and Erin Foster, who have a lot of famous friends) and “public clips” (those Instagram videos) with the delight and faint ostentation of someone who has just learned a foreign language.

Previously, she had little patience for workout fads. A decade ago, as an instructor at various barre method gyms, she was scolded for substituting in moves, such as lunges, that she considered more effective.

She created Refine (which has a devoted, though not boldfaced, following) after a year spent grilling sports scientists and professional athletes’ trainers about what got results. Mike Boyle, whose clients include N.F.L. players and other elite athletes, told her she was right about the lunges.