I was going to say that it isn't possible, but I did figure out at least one way to sort of do it, at least for some images of some waterfalls, with somewhat acceptable results sometimes. Caveat emptor.

The trick I came up with relies on the fact that, in a typical picture of a waterfall, the water looks white while the background is mostly dark. Thus, by using a technique similar to exposure fusion, we can blur the water while keeping the background sharp. Also, as long as the water is all mostly moving in the same direction (down), we can more or less get away with a simple linear blur — don't try this on a picture of churning rapids.

For a demonstration, let me use this public domain picture of the Pacheco Waterfall in Venezuela by Hellen Perrone at Wikimedia Commons, taken with a shutter speed of about 1/200 s:

   
(Click the images to view them at full size.)

The first step is make a copy of the image on a new layer, and to cut away anything that is (close to) white except the waterfall. In this photo, that mostly means the sky:

   
(Here, as in the images below, transparent areas are shown as black.)

Next comes the trick: add a layer mask to the new layer, and set it to a grayscale copy of the layer. This effectively makes the dark (non-waterfall) parts of the layer transparent, while leaving the light (waterfall) parts opaque:

   
(Again, the layer is shown on a black background. Here's a small transparent PNG version, if you prefer.)

To better separate the waterfall and non-waterfall parts, we need to increase the contrast of the mask. To do that, I selected the mask and adjusted its color levels using a strong S curve:

     
(Here's another transparent PNG for those who like them better.)

After applying the layer mask (to merge it into the alpha channel), we're ready to add some motion blur. Here, I used a linear blur with a 50px blur length (quite large, to make it obvious even at small sizes) and an angle of 265 degrees (5 degrees off straight down):

   
(And here's a transparent PNG version of this step too.)

Replacing the black background with the original photo, the combined image looks like this:

   

Finally, a bit of manual erasing fixes a few inappropriately blurred spots, producing this result: