I've been doing this for 50 years, and I've seen thousands of business cards. I can’t remember seeing one with a person's degree field on it. Someone that has your card has it for a reason, and knows what is your field.
I know you've just completed a rigorous academic program, but there are lots of MS programs out there that have little content, and therefore, there are lots of people with MS and MBA degrees. When you refer to your degree, do it in a context where you can demonstrate that you’ve been through a rigorous program, and why that makes you more qualified than someone else. Elaborate on your degree in your Vita. There you have room to go into a bit of detail, and explain your qualifications.
On your business card, just:
John Smith, MS (or Ph.D, or RPE, or whatever)
Be sure there's a QR code on the back of your card that will take the recipient to a web page that shows your qualifications in detail. I’ve got 2 QR codes on the back of my card. One is an eCard and one is a URL that takes you to my web page. VERY important is the no-nonsense appearance, spelling , and grammar of your web page.
You’re at an exciting time in your life. Your concern with detail is a very good sign. I envy you and wish you the very best of luck.