The fuselage of flight AA 331, carrying 154 people from Miami, broke apart after the incident at Norman Manley International Airport.
Jamaican officials said 44 people had been taken to nearby hospitals for treatment. Four were seriously hurt.
The plane came to a halt just 10-15ft (3-5m) from the sea.
American Airlines spokesman Tim Smith said the fuselage of the Boeing 737-800 was cracked, the right engine had broken off and the main landing gear had collapsed.
The plane, which had originated in Washington DC, was carrying 148 passengers and six crew.