He set up the hangar-size white-box building, called the Galería Jumex, as a museum, and it still functions as one. It’s currently filled with a terrific corporation-needling survey of work by the Danish collective Superflex, whose members have proposed that museums should pay visitors to enter, not the other way around. The space also serves as headquarters for the Jumex Foundation, which sponsors education initiatives and distributes art grants.

But with its distant location and strict security precautions — visits are by appointment only — the Galería has attracted scant traffic. The new Museo Jumex, by contrast, is right in the center of town, open long hours and geared to walk-in trade. The old museum was an insider secret; the new one is attracting all eyes.

Given this bid for high visibility, the new museum’s almost recessive exterior comes as something of a surprise. Designed by the British architect David Chipperfield, the three-story building is a plain, compact block of light travertine, unornamented apart from a saw-tooth crest on top. It’s a no-nonsense, no-ego structure that seems to look inward rather than outward.

In a way, this is understandable. The museum is dwarfed by a forest of new condominium towers behind it. And it’s visually upstaged by the look-at-me design of another museum across the street: the hourglass-shape Museo Soumaya, opened in 2011 by the Mexican billionaire Carlos Slim Helú to display his own collection, a smorgasbord of European art from the Renaissance to Rodin, with Mexican work folded in. (Mr. Slim, who owns the condo towers, sold Mr. Lopez the land that the Jumex is on.)