If the credit card has a balance, your credit score will definitely drop after you close the card. That's because 30% of your credit score is based on your credit utilization - the amount of available credit you're using. When you close a credit card, you have no available credit, so your credit utilization shoots up to 100% immediately. As a result your credit score drops.
Even if you the credit card you close has a zero balance, your total credit utilization - which considers all your credit card balances and available credit. If your other credit cards have balances above 30% of the credit limits, closing a single credit card could hurt your credit score.
If you have no other credit cards, or your only other cards are store credit cards (and you're closing a major credit card), your credit score could drop. Mix of credit is 10% of your credit score and looks for your experience with different types of credit products, including both credit cards and loans.
Closing your oldest credit card could impact your credit score in terms of credit age (15% of your credit score). But not until that account drops off your credit report after about 10 years or so.