The mine is surrounded by Kakadu National Park and is located about 230 kilometres east of Darwin.
The Ranger mine's operator, Energy Resources of Australia, says the leak occured at 1am.
Workers were evacuated before the tank burst and "a mixture of slurry escaped".
"Upon discovery of a hole in the side of the tank, personnel were removed from the nearby area before the tank failed and a mixture of slurry escaped," ERA said in a statement.
"The slurry moved outside the bunded containment area, but has been captured and contained on site. As the material was contained within the processing area there is no impact on the environment surrounding the Ranger Project Area."
Traditional owner groups say they hold fears about the potential environment impact on Kakadu National Park.