The picture, which has since been pulled from the social networking Web site, showed 27-year-old Jon Favreau and another man in an "Obama Staff" t-shirt posing with the woman Obama has tapped to be the next secretary of state.
Clinton spokesman Philippe Reines told ABC News that "Senator Clinton is pleased to learn of Jon's obvious interest in the State Department."
Favreau has apologized to Clinton via her staff. His apology was "absolutely accepted and appreciated," Reines said.
The Obama Transition Team did not comment.
ABC News contributed to this story.