I have looked into this before and there is no definite answer ; there does not seem to be a reason.

Here is a discussion listing a number of possible answers. I like the idea that it is a corruption of the word "frock" which is the vice luthiers use to hold and shape the frog.

http://www.violinist.com/discussion/response.cfm?ID=8725

PS You mean the base of the bow. The tip of the bow is the other end. The frog is where you hold it.

Not sure, but it may be German, and really mean the hoof of a horse. sort of shaped like that.

Or, alternatively, the French invented the modern bow... (sorry)

Its not. The tip of the bow is called the tip. The square-like part on the other end is called the frog. I have no idea why.

i don't know. i doubt it has to do with the shape, because i don't think it resembles a frog! i have always wondered that.

not answering, but i agree, idk

The bottom part of the bow..the black part is called the frog..
The bottom part of the violin, decorative swirl is called a scroll
I honestly don't know why they call the bottom part of the bow a frog...I have played the violin most of my life--the frog looks nothing like a frog..unless some of the baroque perhaps do.