The footage offers a drone's eye view of the large volumes of the museum, which appear to burst through the rockface of Mount Kronplatz at 2,275 metres above sea level.
Fonk's footage shows off the museum's curved forms. One cantilevers over the valley, while two others form windows, offering views from the underground galleries.
More glass-reinforced fibre concrete forms emerge from the ground to create canopies that frame the building's entrance.
The museum is the final instalment in a series of six mountain museums in South Tyrol commissioned by Reinhold Messner – the first climber to reach the summit of Mount Everest without additional oxygen.
It explores the history of mountaineering – displaying objects, images and tools in galleries organised over three floors and connected by cascading staircases. The building also includes a small museum shop and a 20-seat cinema.
Zaha Hadid first unveiled the design for the Messner Mountain Museum Corones in 2013 and it opened in July 2015, becoming the Pritzker Prize-winning architect's third project in the Alps.
The plans for the subterranean museum currently feature in an exhibition called Made in Italy at the MAXXI in Rome. The show, which marks the one-year anniversary of Hadid's death, explores the architect's long-standing relationship with the country.
The footage of the was captured on a DJI Mavic Pro drone by Alaïa Fonk and edited by Dezeen.