The galaxy, the first of its kind to be detected, has been named VIRGOHI21, and is 50 million light years away.
It could only be found using radio telescopes because there are no stars to give light.
A dark galaxy is an area in the universe containing a large amount of mass that rotates like a galaxy, but contains no stars. Similar objects previously discovered have turned out to contain stars when studied with high-powered telescopes, while others were the remnants of two galaxies colliding.
But when the international team of scientists studied their find, they uncovered no visible trace of any stars and no nearby galaxies which would suggest a collision.
Dr Jon Davies of Cardiff University said: "The universe has all sorts of secrets, but this shows that we are beginning to understand how to look at it in the right way."