The boxy brown suitcase-shaped pavilion, covered with the brand's signature stencilling, was erected 10 days ago just outside GUM, a 19th century upmarket department store.
It lies across the square from the Kremlin, and many tourists and Russians complained it was blocking views of most landmark sites.
The once omnipotent Communist Party was outraged by its proximity to Lenin's tomb, and preservationists stressed that Red Square is a Unesco World Heritage Site.
On Wednesday, following several days of furious media commentary, the GUM store said it had asked Louis Vuitton to take down the pavilion.
It was never entirely clear who had granted permission as the square is under official jurisdiction of the Kremlin.
But a Kremlin source told Russian news agencies that the structure was "not agreed with the presidential administration".