The pair were given free rein to assemble pieces from the vast collections and archives of the museum, as well as some of its partner institutions, in order to put together the six-month show, entitled "Spitzmaus Mummy in a Coffin and Other Treasures".
The opening of the exhibition on Monday evening was attended by some of Anderson's perennial collaborators such as actors Jason Schwartzman and Tilda Swinton.
Tongue firmly in cheek, 49-year-old Anderson gave a short speech describing the process of putting the exhibition together with Malouf, 43, as "the culmination of several years of patient, frustrating negotiation, bitter, angry debate, sometimes completely irrational confrontation and often Machiavellian duplicity and deception."
"Perhaps I am as guilty as she is -- but I doubt it," he added.
Even before they started working on the project in early 2015, Anderson and Malouf had been frequent visitors to the museum, which boasts one of Europe's most extensive collections of fine art.
However, anyone expecting a traditionally didactic museum experience, centred around a historical theme for example, will be disappointed.
With labels and explanations cast aside, the visitor has the impression of stumbling into an intimate and sometimes surreal space, crammed with objects which evoke the palette and symmetry that Anderson fans will recall from films
such as The Royal Tenenbaums, The Grand Budapest Hotel and Moonrise Kingdom.
"It feels like the collecting chamber of an eccentric count, somewhere in the Czechoslovakian countryside hundreds of years ago," Jasper Sharp, the museum's curator for Modern and Contemporary Art, told AFP.
Many of the pieces displayed are indeed fit to grace any aristocratic mantelpiece -- a delicately worked ivory sculpture of a phoenix, or a medieval games board inlaid with mother of pearl.
But they have not been chosen according to traditional notions of rarity or artistic prestige.
The show's eight rooms are arranged instead in a more intuitive way and objects that may hitherto have been overlooked take centre stage -- such as the tiny coffin of the show's title, made in ancient Egypt for a shrew.
Sharp says Anderson and Malouf "curated very much with children in mind, both in the selection of objects and the manner in which they displayed them.
"There are objects hiding high up, low down, every time you come into the exhibition you'll see something different."
The show is the third in a series of exhibitions curated by modern artists which form part of the museum's efforts to engage with contemporary art.
Could the museum be accused of seeking the publicity that will go with bringing in a high-profile name?
"You will always lay yourself open to the charge of making noise when you invite someone in like this," Sharp admits.
"On the other hand Wes and Juman... certainly didn't see themselves as being an instrument of fame and attention-grabbing, very much the other way around, they saw it as a huge honour to work with the museum."
"Our hope is that our objects develop these layers and skins of meaning through their reinterpretation," Sharp adds.
The exhibition will run until 28 April 2019 and will transfer to the Fondazione Prada in Milan next autumn.