It depends
Rice miso (kome) and soybean miso (mame) are gluten-free. Barley miso (mugi) is not, and the fermentation starter can also be grown on barley. The variety is often only stated in Japanese on imported jars.
Soybeans fermented with koji, a mould grown on a starchy substrate. The substrate is the whole question. Grown on rice it gives kome miso; grown on barley it gives mugi miso; grown on soybeans alone it gives hatcho miso. All three are sold simply as miso in most shops, and the paste looks much the same in the tub.
Because barley enters through the culture rather than the recipe. Somebody reading an ingredient list for grains will see soybeans, salt, koji — and koji is not a grain word. It is a mould, and the grain it was grown on may not be named at all.
White and yellow miso are usually rice-based; the darker, maltier red and brown ones are more often barley. That is a tendency and not a rule, so the reliable move is to buy a miso that states its type or carries a gluten-free claim, and keep that one. Miso also hides inside things — dressings, glazes, ramen broth — where the type is never stated.
CiCi treats miso as conditional and clears it on a gluten-free claim rather than on the word miso. It also tracks koji as a synonym, because that is the term that actually appears on the better labels and the one most likely to be read past.
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 Miso 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.