I presume you're concerned about the single horizontal line of noisy pixels, not the "normal" high-ISO uniform "background" noise (technically: statistical quantum mottle) throughout the frame.
Is that line at the same location on every frame? On your sample image it's at 36.3 % of the vertical image space. If it is always at the same location, and if it increases in intensity as you raise your ISO setting, it may be an indication of a failing image sensor. More specifically (on a CMOS sensor) a "row analog processor" or "row decoder". If it moves (occurs at random locations, It can indicate a failing clock circuit or interfering electronic noise from another source. The image you posted has been compressed by the website so it's hard to see exactly what the data looks like, but at first glance it appears to be random variable intensity noise along one scan row only, even though the convolution filter applied in-camera to reduce (smooth) the normal sensor noise has spread the excessively noisy row out over 4 or 5 rows.
This "row only noise" is not normal for your camera at ISO 6400. Again, if it's always at the same location, it's most likely a physical issue in the sensor array. If it occurs at a random location on successive frames, there are a multitude of possible causes including a faulty DIGIC 6 main processor.
Ideally, a RAW image data set should be checked, since any processing of the image such as converting it to a jpeg image will spatially filter the data and make it more difficult to determine what is actually happening.
