A release from the Metro Nashville Police Department says Davis was stopped early Friday for speeding downtown.
The arrest report stated when the officer pulled over Davis' car, the player smelled of alcohol and his eyes were watery. Davis consented to a breath alcohol test, which registered 0.11. The level of intoxication in Tennessee is 0.08.
Davis is recovering from a hamstring injury and did not travel with the Titans to a preseason game on Friday night at Dallas.
Davis' agent, David Butz, could not immediately be reached for comment.