Maybe. It depends on your state and whether the driver’s license you’re issued is in compliance with the REAL ID Act, which since 2005 has been a federal standard for photo identification.
Beginning on January 22, 2018, domestic air travelers from states that are not compliant and have NOT been granted an extension will need to show an ‘alternate form of acceptable identification“, of which one is a Passport (book or card).
Beginning on October 1, 2020, ALL domestic air travelers will need a REAL ID compliant driver’s license or one of the aforementioned acceptable methods of identification.
Remember that if you leave the U.S., you’ll still need a Passport to return – that won’t be effected by the REAL ID Act.
Here’s a great explanation of the REAL ID Act
And from Homeland Security, some FAQs about REAL ID and travel:
Here’s where you can check to see if your state issued driver’s license is compliant with REAL ID: