It is possible. Depending on the size of the bomb, the volacano could collapse in on itself and plug itself up. The tremor or shock could cause the tube of magma coming up to close, or could close or otherwise affect the fault below. Perhaps the fault would lengthen and the magma, ash, etc would flow somewhere else and come up there. If the bomb was powerful enough and the eruption small enough maybe all the magma and other ejecta would be vaporized. But on the other hand it could make it worse, even if we just ignore the effects of a nuclear blast itself. Instead of collapsing and plugging the volacano it could blast the walls away and release an entire crater's worth of molten lava or change the flow path. The blast could open the tube or the fault allowing even more magma to rise. It could loosen or vaporise solidified plugs in other tubes, or open connections to other 'pockets' of magma. It could change the shape or direction of the faults, allowing a new volcano to erupt in an even worse place. It might have no real effect on the volcano itself other than to make the lava radioactive, and go flowing off to become a solidified radioactive lava flat. Radioactive ash could spread all around the world,coming down nearby as radioactive ash fall, farther away as radioactive rain, contaminating ground water and the earth. All in all not such a good idea. Please do not submit the idea to the government. I can see FEMA making plans to use WMD's as soon as possible in as many situations as possible.. Why, we could drop one into the next hurricane, we could drop one into a flood and instantly vaporise all that terrorist water. The possibilities are limitless.

No, because volcanoes are not turned on and off like a switch. This may have made a storyline in a B-movie in the 50s and 60s, but in real life things are different. A volcano erupts because pressure has built up in a chamber located underground - the magma chamber. The eruption is the mechanism by with the pressure in the chamber is relieved. Plugging the vent through which the magma is rising will not remove the pressure. Underground nuclear tests usually produce one of two results. If the nuclear device is fairly close to the surface, the explosion creates a large cavity which then collapses because the roof is inadequately supported. This creates a crater at the explosion site. If the explosion is deeper, it produces a (roughly) spherical cavity. Much of the rock and earth in the immediate vicinity of the explosion is vapourized or, as the distance from the centre of the blast increases, is melted. This material collects at the bottom of the cavity where it gradually solidifies. The earth and rock around the blast crater or cavity is usually badly fractured. Such an explosion would have no effect on the magma flow, since the material melted by the blast does not cool instantaneously. The magma would be able to find its way through the newly molten rock to the surface. In addition, the fractured ground could provide new magma channels. Even if this scenario did work, plugging the channel(s) leading away from the magma chamber would cause the pressure in the chamber to rise until it is relieved in some manner. Relief might come from the formation of another channel from the chamber to the surface. On the other hand, it might lead to a catastrophic explosion, such as that which occurred at Mount St-Helens or at Krakatoa. This does not even address the issues arising from using a nuclear device near or upwind of populated areas.

The answers by Redjohn and Notmrjohn are very good and cover most scenarios, I would just like to add one little piece of...whatever. If an enormous eruption was building up, like those of Krakatoa or Tambora, with the equivalent of 3,000,000 Hiroshima sized bombs at Tambora, an event which affected weather worldwide and killed many, it might have some positive effect by blasting earlier, before it actually erupts, in a semi-controlled release of the pressure which might cause an eruption. Perhaps a better idea, though, is to drill vents with automated remote control drilling equipment, rather than risking radioactive dust being spread earthwide. At Tambora there is some indication that pressure is again increasing, with a sub-surface blast, near the surface, it could cause fissures large enough to release the gases trapped inside and prevent an eruption of greater magnitude. The caldera, 15 mile long and 4000 feet deep, should contain pretty much any effects of the blast, and if the depth is calculated precisely to come very near the surface without completely obliterating it, there may be very little dust released. But, these are just the musings of an idle mind, I would not recommend using a nuclear device for any purpose, they should all be shot into space and destroyed, along with those who build them. (LOL?) The desired effect is to cause an eruption, but a small one, preventing the pressure from building up to the point of creating a huge one. Problem is, we can't estimate how big it will be, if it would have erupted 10 mins after the nuke anyways, if a vent will form and release the pressure all on its own, with no radioactivity. Man just doesn't know all the factors, and never will, so we just shouldn't interfere. We usually just make things worse. The example of the hurricane, maybe if we did stop the hurricanes, besides the radiation, what effect will that have on weather world-wide? We can't even determine, to any reasonable consensus, if global warming will lead to heat waves or ice ages, or both, or where.

It would be like throwing gas on a fire to put it out.

Stop?It would rather affect the areas that are far beyond reach of the volcano.Volcanoes are nothing but openings in earth's crust where earth's releases it's magma pressure and ejecting magma.Dropping a nuclear bomb would let the volcano spread to the areas which don't come in the path of the lava flow.Trying to bring about an alteration in natural phenomenon is not a wise decision. . It's just like treating an infected sore on your body filled with puss with a gunshot.Would that relieve the pain due to the sore?

Some have toyed with the idea of detonating a nuke in a volcano to pacify it forever, believe it or not, but putting a nuke to a volcano is like putting a Glock to a pimple. Sure, you'd get rid of it, but be in for a hell of a trade-off.