I am looking at this from the perspective of your members.
You are saying this is to discourage membership now that you are at your desired enrollment. Not that your costs have increased or that you now desire to give yourself a raise or your staff a raise. It may irritate your clients if the increase is substantial and it may not do the trick.
Do you have trouble telling people “no”? I used to use my rates as a deterrent to new clients so that I didn’t have to tell people “I don’t want any more clients”. I wanted to keep my free time for me and my family. But this often didn’t work and I felt like I was taking advantage of the people I was charging such a high fee.
I now simply tell people that I can’t fit anymore clients into my schedule and that I can put them on my waiting list for the next available slot. My rates are near the top of my market now and I don’t want to scare away people that need my help so I use a rate range as opposed to a set rate.