No, this comes from a gluten grain
Brewer's yeast is typically a byproduct of beer brewing and carries barley protein. Distinct from nutritional yeast and baker's yeast, which are gluten-free.
Yeast recovered from a brewery after it has finished fermenting beer. The organism itself is ordinary Saccharomyces cerevisiae and contains no gluten — the problem is not the yeast, it is what the yeast has been sitting in. Barley protein from the wort comes with it, and that is what ends up in the supplement or the flavouring.
Because three unrelated things are all called yeast, and only one of them is a problem. Baker's yeast is grown for the purpose and is fine. Nutritional yeast is grown on molasses and is fine. Brewer's yeast is a brewery byproduct and is not. A label saying "yeast" means the first of those; the risk only arrives when the word brewer's is in front of it, or when the word is yeast extract, which is tracked separately because it can be either.
Worth knowing because brewer's yeast turns up outside food. It is sold as a B-vitamin supplement, recommended in some contexts for lactation, and used in savoury flavourings — places where somebody managing a gluten-free diet is not necessarily reading as carefully as they do in a supermarket aisle. Debittered brewer's yeast is still brewer's yeast; the bitterness was removed, not the barley.
CiCi holds these as four separate entries — baker's yeast, nutritional yeast, brewer's yeast and yeast extract — rather than one entry about yeast. Collapsing them would be tidier and would get the answer wrong in both directions at once.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
The aisle guides below cover Brewer's yeast in context — which is usually the more useful question, because an ingredient rarely appears alone.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.