According to this site, a typical tornado has a kinetic energy of 3 x 10^12 J = 3 x 10^19 ergs (http://www.dartmouth.edu/~ears5/handouts/TornadoEnergy.html)
The Atomic Rockets "Boom Table" (http://www.projectrho.com/public_html/rocket/usefultables.php) gives us the equivalent amount of energy in a weapon: 1 X 10^19 J is roughly 3 Gt (three billion tons of TNT). By comparison, the Tsar Bomba was 50 Mt, and the largest ever US nuclear test; Castle Bravo, was 15 Mt.
Generally speaking, I would suggest that the proposed cure is somewhat worse than the problem.
The trick here isn't about how much energy is applied, it is more about where and how it is applied.
Read this article and it gives a good introduction to how tornados work: http://thevane.gawker.com/what-is-a-supercell-thunderstorm-1564133584
Here is the weather radar image of a Tornado
The trick to "killing" the tornado isn't nuking it directly, it's about breaking apart the cycle that feeds it. It's by nature an unstable system so injecting energy into the downdrafts or cutting off energy from the updrafts would be the way to go about stopping it.
Unfortunately the storm systems are just not well enough understood to say just how much energy is needed, but it's far lower than that contained in the storm. A relatively small amount of energy in the right place will have effects right across the process.
However putting more energy into the wrong place would actually make the storm stronger, such as by fueling the updrafts.
Hmmm... on its own, a missile or bomb would not affect it. Tornados are vortexes produced by wind. Perhaps the force of a sufficient explosion may counter these winds and disrupt the vortex, ending the tornado.
I hope it's not to close to civilization, because I think the explosion will need to be very powerful.