He told his department that his deputy, Rebecca Blank, would serve as acting secretary.
"In my personal capacity, I will continue to do everything I can to support the President and America's businesses as they continue to advance innovation, US competitiveness, and prosperity for our people in the months and years ahead," Bryson wrote.
Bryson, 68, has been on medical leave since June 11.
On the evening of June 9, police found him unconscious at the wheel of his vehicle after the second of two minor collisions in southern California.
His staff later said that he had suffered a seizure, without giving further details. It was the first time he had had such an attack, according to one Commerce official cited by Fox News.
Bryson was cited for felony hit-and-run for the first of the collisions, but no charges were formally filed.
In a statement, Obama paid tribute to "an effective and distinguished leader" who "fought tirelessly for our nation's businesses and workers."
Bryson – who was picked by Obama despite Republicans' objections, the BBC noted – was commerce secretary for less than a year, having been sworn in in October 2011.