Rye is one of the three gluten grains it contains a protein called secalins, which is a form of gluten. Therefore, any food containing rye as an ingredient is most definitely not safe on the gluten-free diet.
It gets trickier when we address rye whiskey, as you'll see in a minute.
In baked goods that use flour, you'll mainly find rye in sandwich bread for example, it's common in German and Eastern European countries to use rye flour in bread with caraway seeds, and in pumpernickel bread. In addition, crackers and crisp breads frequently contain rye, and those that do also are off-limits for someone with celiac disease or gluten sensitivity.
Food labeling laws do not require disclosure of gluten on labels, but in practice manufacturers generally will want you to know that there's rye flour or rye grain in a product. Therefore, if you see mention of rye (or its Latin name, secale) on a label, you should steer clear of that product.
Triticale is a hybrid of rye and wheat, and also contains gluten.
For those who crave that dark bread taste and texture, some gluten-free manufacturers make gluten-free "rye" breads.
For example, Three Bakers offers a gluten-free rye-style bread, and Canyon Bakehouse makes Colorado Caraway, a gluten-free sourdough mock rye bread. Both these brands have very stringent standards for gluten cross-contamination their products are tested to make certain they include fewer than 5 parts per million of gluten.
Rye Whiskey Considered Safe By Some, But Not All
Now, back to the question of whether rye whiskey is gluten-free or not.
Rye whiskey is made from rye grain in fact, in the U.S., the mash to be distilled must start out life as at least 51% rye to qualify as "rye whiskey."
Since rye whiskey is distilled, many celiac disease associations consider it to be gluten-free; the distillation process theoretically breaks down and removes the proteins that cause our reactions.
However, some celiacs or gluten-sensitive people (it's not clear how many) actually have strong reactions to alcohol distilled from gluten grains. In my experience, symptoms of a gluten reaction to these alcoholic beverages often include inebriation and a hangover that are wildly out of proportion to the amount of the alcohol you actually consumed, coupled with more conventional glutening symptoms, such as diarrhea or constipation and brain fog.
I react this way myself, and I can tell you, it's profoundly unpleasant. However, other people report that they can drink distilled gluten grain-based alcoholic beverages without any problem reactions are very individual.
Still, I urge you to proceed with caution if you want to try rye whiskey, especially if you seem more sensitive than average to trace gluten. You can read more about this in my article Is Alcohol Gluten-Free?
Finally, in the U.S. at least, the regulatory agency for alcoholic beverages won't allow alcohol made from gluten grains to use a "gluten-free" label or to make gluten-free claims. This isn't something I've ever seen with rye whiskey (the rules were aimed more at beer makers), but you might want to take a look at the reasoning behind this ruling: Labeling Rules for Gluten-Containing Alcoholic Beverages.
The bottom line: Avoid rye bread and crackers (or substitute gluten-free "rye-style" products), and tread carefully when trying rye whiskey.