The 26-year-old American weighed in at 140.4 pounds and had two hours to lose the 0.4lbs but failed to return to the scales.
He was due to defend his belt against Theophane in Washington.
The fight will still go ahead, but only the 35-year-old Briton will be eligible to win the world title.
It is the second time Broner has been stripped of a world title.
He lost his WBO super-featherweight title in 2012 for failing to make the weight for his bout against Vicente Escobedo.
Adrien Broner has been stripped of his WBA light-welterweight title after failing to make the weight for Friday's fight with Britain's Ashley Theophane.