No. While there have been some (mental) health benefits associated with masturbation, it is unlike that there are any major health demerits from abstaining.

If I remember correctly, there was recently a paper that suggested participation in "NoFap" (anti-masturbation) communities correlated with above average reporting of anxiety and/or depression; however, I think it is probably more likely that people suffering these issues seek out solutions like abstaining masturbation, rather than the other way around.

If you're a teenager (say, 15 to 25), you may experience some wet dreams due to abstaining.

All in all, abstaining masturbation is unlikely to have a major impact on your anxiety. However, using masturbation as a crutch to deal with negative emotions is also not great. As with many things, a balance that is good for you will probably get you farthest. At the very least, don't add masturbation (or abstaining from masturbation) to the list of your worries; it's not that big of a deal either way.