The insurgents, members of the Islamist fundamentalist group al Shabaab, are now searching the wreckage.
"We fired at an American plane spying for information over Kismayo.
Our forces targeted the plane and shot it and we saw the plane burning. We think it fell into the sea," Sheikh Hassan Yacqub, spokesman for the al Shabaab rebels in Kismayo, was quoted by Reuters.
"We are still searching for it," he said.