The Fairfax County School Board, citing Reagan Administration plans to slash federal aid to localities with large military populations, has warned federal officials it may stop educating 1,520 children of personnel assigned to Fort Belvoir.

Board members, who approved the decision late Thursday night, said alternatives might include charging tuition to parents or the federal government or turning administration of the base's three elementary schools back to the Army unless $4.4 million in aid to the county is left intact.

The decision was relayed to the secretary of the Army, the secretary of education and the commanding general of Fort Belvoir in a letter signed by Board Chairman Ann P. Kahn.

The so-called impact aid compensates local school systems for the cost of educating children whose parents do not pay local income or real estate taxes because they live or work on federal property.

Although critics charge that affluent school districts such as Fairfax can afford to absorb such costs, county officials say the aid pays only about half of the average $2,833 per pupil expense of educating the Belvoir children.

Fairfax school officials conceded that under the Reagan budget now before Congress, the federal dollars once expected for the autumn of 1981 may not materialize.

"The situation looks absolutely grim," Myron Cale, the school system's budget director, told the board.

School board chairman Kahn told fellow board members that at least 17 other states are now considering legislation to authorize local school districts to charge tuition from military families. The Virginia General Assembly passed such a law last year.

Federal officials have countered by threatening to obtain court injunctions to prevent the tuition from being charged, a challenge Cale said Fairfax could be confident of winning in court.