Once deployed, the nuke will have a few second delay before detonating. Once it does, the resulting explosion will cause significant damage to all tanks and destructible objects within a very large radius (usually the whole map, depending on the size).
There are only a few ways to avoid being damaged by the explosion. The player may get lucky and happen to be far enough away from ground zero if they are playing on a large enough map. The explosion also does not affect any tanks underground. The player can also use a Teleporter powerup right before the explosion shockwave reaches them and avoid it completely.