It depends on whether your credit card issuer reports the missed payment to the credit bureaus. Maybe they will, or maybe they won't, but you should assume they will. One missed payment isn't likely to put you into the bad credit category if you're currently in the good credit category. It usually takes a series of missed payments or some other blemishes on your credit combined with a missed payment to do that. A missed payment certainly isn't going to do anything good for your credit, so you should still do everything in your power to make your payments on time.
Keep in mind that missing a payment will make next month's bill that much bigger. You'll owe this month's payment, plus next month's payment, plus any late fees the credit card issuer charges. Being late with a payment can also end any promotional deals you might have. That 0% APR for 12 months? It's likely to be gone if you miss a payment. So even if it doesn't hurt your credit, missing a payment will hurt your wallet.