State Department spokeswoman Jen Psaki did not provide any details about the suspect, who had been identified in a New York Times report as a man in his 20s from Florida and of Middle Eastern descent.
"I can confirm that this individual was a US citizen," Psaki said, adding that he was "involved in a suicide bombing inside Syria."
Western powers have expressed concern that some of their citizens have traveled to fight in the civil war in Syria, some of them joining extremist groups that might one day seek to strike their home countries.
The video, reported by the private terrorism watchdog SITE Intelligence Group, depicts a huge explosion as well as footage of a young, bearded man cradling a cat and identified as the attacker.
The bombing is thought to have taken place on Sunday. The New York Times report cited US officials as saying they thought it was the first such suicide attack to have been carried out by an American.