"The situation is pretty much under control, there have been no fatalities and the injured are being cared for," Jamaica's Information Minister Daryl Vaz told journalists.
CNN said four of the passengers were in serious condition, but American Airlines said preliminary reports indicated there were no serious injuries. Some of those taken to the hospital were treated for shock.
One passenger told a local radio station in Kingston that the flight was "bumpy along the way and the landing was terrible.
"The plane did not seem to be slowing down when it landed. There was a loud sound, then a huge thud and then we started to feel rain coming through the top," he said.
Jamaica has been badly hit by rain and flooding in recent days.
The Jamaica incident is the second runway mishap for American this month. On December 13, the wing of an American MD-82 struck the runway in Charlotte, North Carolina, while landing, causing damage to the plane. No one was hurt.


