The robot - which resembles something from a car assembly line - will build new sections of the Elytra Filament Pavilion over the coming months.
The futuristic structure will grow and change shape using data based on how visitors interact with it.
It was unveiled on Wednesday to mark the launch of the V&A's Engineering Season.
The museum's director Martin Roth described the pavilion as an example of "creative engineering".
Elytra's canopy is made up of 40 hexagonal cells - made from strips of carbon and glass fibre - which have been tightly wound into shape by the computer-controlled Kuka robot.
Each cell takes about three hours to build. On certain days, visitors to the V&A will be able to watch the robot create new cells that will be added to the canopy.
Speaking at the launch event, architect Achim Menges said the pavilion's design was inspired by fibrous structures found in nature - in this case, the hardened forewing of a flying beetle known as the elytra.
"Everything that is above your head is made from those materials only," he said, waving a handful of flimsy carbon fibres.
"These materials require a different mindset, because your standard construction materials are very difficult to put in your pocket."
As a result, the structure is remarkably lightweight. Each cell weighs 45kg and has a predicted lifespan of 50 years.
Menges says that makes the canopy ideal for construction projects such as stadium roofs.
Importantly, given the British climate, the robot can also work in the rain.
"As you can see, the cover is absolutely weatherproof!" Menges said at Wednesday's wet open-air launch.
The Elytra Filament Pavilion is at the V&A in London 18 May - 6 November
A robot has taken up residence at the Victoria & Albert Museum to construct a new installation at its London gardens.