The "cloak", described in the journal Science, hid an object from detection using light of wavelengths close to those that are visible to humans.
Previous devices have been able to hide objects from light travelling in only one direction; viewed from any other angle, the object would remain visible.
This is a very early but significant step towards true invisibility cloaks.
Tolga Ergin, a scientist from the Karlsruhe Institute of Technology in Germany led the study.
He told BBC News that his team's cloak was based on the concept that you can "transform space" with a material.
He and his colleagues designed a photonic metamaterial, which influenced the behaviour of light rays.
"You can think of any transformation that you would like to have, and tailor your material to mimic this," he explained.
The basis of the design is known as a "carpet cloak". This was first proposed by Professor Sir John Pendry from Imperial College London, who also took part in this study.
"He proposed the theoretical design of having an object hidden under a bump and making the bump disappear," said Mr Ergin.
"It's like a carpet mirror," he continued. "If you hide an object under it, there is a bump, so you see a distortion in the reflected image.
"We put the carpet cloak on top of that bump and it bends the light so that the distortions disappear.
"You have the impression that the mirror you're looking at is flat."
The trick is to change the speed and direction in which light travels through the material - that is, to change the material's refractive index.
The researchers achieved by this using a polymer crystal made up of very tiny rods. "By changing the thickness of the rods, you can change the ratio of air to polymer," explained Dr Ergin.
"Since the refractive index of air is about one and the refractive index of the polymer is about 1.52," he explained, "in principle, we can get any refractive index between those two numbers," he said.
By tailoring the refractive index of the the surface of the bump, the scientists rendered it invisible to a wide range of light wavelengths slightly longer than those that we can see.
As a result, under this light, the reflective surface appeared to be flat.
A similar effect has been achieved previously in two dimensions - changing the refractive index of a piece of silicon by drilling tiny holes in its surface.
But, these holes can only be drilled in one direction.
"So if you at look at the thing from [any other] angles, you immediately see it," said Mr Ergin.
In this case, the team used a technique called laser writing to create their 3-D cloak. This uses a very finely focused laser, to "write" into a light-sensitive material.
"Wherever you put the focus spot into the material, it will harden," explained Dr Ergin. "It's a similar process to photography - when you develop it, whatever hasn't been exposed to the laser will be washed away."
The carpet cloak was originally designed to work in two dimensions. But when Dr Ergin and his colleagues calculated how the rays of light would travel through an object, they realised that they could use their technique to build a structure that would work in three dimensions.
In this case, the researchers use the device to cloak a bump one micrometre (one thousandth of a millimetre) high.
"But in theory there are no limits [to the size of the object you could hide], said Dr Ergin. "You could blow this up and hide a house.
"But it took us three hours to make this structure, so if you wanted to make it even one millimetre in size you would have to wait a very long time."
Professor Ortwin Hess from the University of Surrey in the UK said that this study was a "huge step forward".
"The really remarkable aspect is the demonstration of invisibility in three dimensions."
One of the major challenges that remains in the design of cloaking devices is hiding objects from wavelengths of light that are visible to humans.
"Photonic crystals usually work because the constitutive elements are not visible to the wavelength by which one observes them," Professor Hess explained.
"So if you look at the desk in front of you, you don't see the individual atoms because they are so small. You just see whole structure - the wood or the plastic."
This means that cloaking devices for visible light would have to be made up of much smaller rods. So for this technique, the laser beam would have to be made even smaller.
Currently, the rods can be made as small as 200 nanometres. To hide a bump from visible light would require rods as small as 10 nanometres.
And, as Mr Ergin explained, there is a limit to how small a point light can be focused down to.
"You could say, 'why not just make [the rods] smaller?' but it's not that easy to scale these structures down. Fabrication techniques have their limits," he said.
But Professor Hess said that this was a great achievement and these photonic materials could be used in the development of lenses and in light storage and optical circuitry.
He added: "We won't have a body-sized invisibility cloak tomorrow but this has demonstrated a remarkable proof of principle."