Many artificial sweeteners are gluten free. The websites for Equal, Splenda, Sweet ‘n Low, and Truvia all specify in the “Frequently Asked Questions” section of their website state that their product is gluten free. The NutraSweet website does not mention the subject.
This is not an unqualified endorsement of artificial sweeteners. There are many problems associated with them. However, apparently they are acceptable for people who live gluten free.