Beginning July 2, the airline will fly only 10 flights each week, down from its current 48. All flights from Dallas, New York, and Puerto Rico will be suspended. Only flights from Miami will continue.
American said in a statement that the decision was financially motivated.
"Since we are owed a substantial outstanding amount ($750m, £442m to March 2014) and have been unable to reach resolution on the debt, we will significantly reduce our flights to the country after 1 July."
Venezuela owes $4 billion in ticket fees to 24 international carriers going back to 2009, and has not acted on its March promise to begin paying the debt, said Jason Sinclair, spokesman for the International Air Transport Assn., headquartered in Montreal, Canada.
American, the largest foreign carrier to service Venezuela, is joining a number of other airlines who have reduced or suspended flights to Venezuela.
Air Canada announced on March 17 that it was suspending flights to Caracas due to concerns about unrest in Venezuela.
Venezuelan President Nicolas Maduro has previously warned that "The company that leaves the country will not return while we hold power."