No. The credit card number that you see in your Account Details page has all but the last 4 digits blanked out, and the card number is coming to that page from a different location than the remainder of your profile information -- in other words, the card info is not stored together with any of your other information.
When you click on "Upgrade/Renew", or go to the Pro Membership order form, you go to a secure page: the web address of that page begins with "https:", and the "s" means secure.
When you make a sale, your commission will be taken out of your credit card on file (0% - 10%, *depending on which shop plan you select). Check out this FAQ to learn about shop options.
You can select your shop plan in My Account, click "Upgrade/Renew" on the right.
(*Though there are no commissions charged for the Ultimate Shop plan, you still need to have a card on file for your monthly fee payment.)