The successful agency will be briefed to redesign the V&A's homepage, www.vam.ac.uk, which acts as the main portal for potential visitors to the museum.
The search marks a shift in digital strategy for the Knightsbridge-based museum, which has tended to appoint agencies to create microsites for its paid-for exhibitions.
In the past, the V&A has worked with the digital agency E3, which it appointed in 2007 to handle the microsite design for a number of its forthcoming shows.
The agency created microsites for the V&A's Surreal Things, Golden Age of Couture and Art of Lee Miller exhibitions in 2007.
Following a three-way pitch later in 2008, E3 was appointed again to handle the design of its Collections website, which enables users to search the V&A's archive of around 27,000 works and 43,000 images.
The museum has also worked with the digital agency Poke, which produced a microsite to promote its Kylie exhibition in 2007.