My guess (looking at your metadata) is that you underexposed it, and the software bumped it up... creating the noise (as someone said)
Why do I think that? Well... You were shooting on Shutter priority, at 1/500th... and your lens was at 2.8 (it's maxim aperture). It's easy to underexpose on Shutter priority, especially indoors.
Make a proper digital exposure (over exposing slightly/"expose to the right.. maximizing data), and then see if the noise is still a problem.
My 5d3 is stellar all the way to 6400 with a properly exposed image.