A credit card company won't process your application if you provide a post office box instead of a physical address. However, some providers do allow you to change your account mailing address to a P.O. Box after you receive the card.
Card Laws
The restriction against processing a card application with a P.O. Box is based on federal law, according to Capital One. It is covered as part of the Patriot Act. While you can submit your application with a P.O. Box, the provider won't process it. You typically get a follow-up call or communication asking for a physical address. This process may delay your approval and card receipt by up to two weeks.
After Approval
After your account is approved and opened, you can contact the provider and change the mailing address on your account to a post office box. However, the company still keeps your physical address on file. The primary reason for the federal requirement of a physical address is to protect card applications and account holders from fraud. When you apply, your physical address and name are compared against government databases to ensure a match.