Elijio Briceno, a former cabinet minister of the Latin American country of Belize, was arrested in Miami by federal drug agents yesterday on charges that he conspired to smuggle monthly shipments of 4,000 to 5,000 pounds of marijuana into the United States.

Briceno, whose People's United Party was ousted in elections last December after 20 years in power, was arrested at a downtown Miami hotel, where he allegedly had gone to pick up a $35,000 advance payment from undercover agents of the federal Drug Enforcement Administration.

DEA Agent Frank Chellino said that during the six-month undercover operation, Briceno, 47, had promised to provide marijuana, airstrips and protection from Belize law enforcement and military officials and had discussed a shipment of 20 to 50 kilograms of cocaine. Chellino said the negotiations with Briceno started while he was still in office. Belize, believed to be the fourth largest supplier of marijuana for the United States behind Colombia, Jamaica and Mexico, has 42 uncontrolled airstrips that are suitable for drug smuggling, Chellino said.

A recent State Department report on international narcotics trafficking said Belize had engaged in successful drug eradication programs in 1983, but those efforts dropped off with the approach of the 1984 election, and cultivation of marijuana doubled.

Just last month, DEA agents in Miami arrested Chief Minister Norman Saunders, the highest elected official of the Turks and Caicos Islands, along with two of his cabinet officials, on charges that the group planned to used the Caribbean islands as a major fueling and transshipment point for smuggling cocaine into the United States.

"The DEA intends to reach out and conduct investigations wherever we . . . legally can, to stop public officials who use their offices to conduct drug trafficking," said Pete Gruden, who heads the Miami DEA office.

The 14-count indictment against Briceno and three other men was handed up by a federal grand jury in Wilmington, N.C., where some of the shipments were to be delivered.