Once deployed, the nuke will have a few second delay before detonating. Once it does, the resulting explosion will cause significant damage all tanks and environmental surroundings 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 catastrophic explosion. The player may get lucky and happen to be far enough away from the epicenter if they are playing on a large enough map. Alternatively, the explosion does not affect any tanks underground. The player can also use a Teleporter powerup right before the explosion reaches them and avoid it completely.