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.
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.
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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.