Concrete objects constructed to look blurred
The first thing that comes to my mind are the works by the contemporary German artist Gerhard Richter. He has a huge body of paintings that are famous for being blurred, like this one:



Or, to a lesser but more photographic extent:



Early 20th century, artists that were part of the futurism movement, wished to portray movement. This might no be exactly what you're looking for, but it does involve blurring, as this is one of the few methods that can be used to depict movement in a static, two-dimensional image (motion blur).
An example is this work by Giacomo Balla, 'Dynamism of a Dog on a Leash':



In sculpture, similar things were tried during the futurist movement. An iconic example is 'Unique Forms of Continuity in Space', by Umberto Boccioni. Again, it does not come across as blurry, because the movement - the blur - has here been solidified:



A similar, recent sculpture is made out of glass shards:



Because it's glass, the outlines are less defined, and the material even changes colour and brightness based on the environment. So not only does it depict blur, the sculpture itself is blurred against its background.

And another recent example of motion blur in sculpture is this work by Ryan Johnson, insinuating a more pixelated or artificial motion blur:



Abstraction is (mainly, arguably) a simplification of form, something that blur results in as well. The problem with sculpture is that it needs solidity, mass, and volume, whereas visual blur, as Elmy mentions, is a visual phenomenon: it's essentially non-physical, non-solid, a mental interpretation. That's why it might be hard to find what you're looking for in a three-dimensional object (although I had hoped to find some sculptures made out of fur, or a similar material, as that has a natural blurriness to it. Like this 



but focused more on the visual quality of fur).