The State Department said yesterday that the Montgomery County Board of Education's decision to charge ambassadors, diplomats and foreign government employes tuition for their children's public school education "could trigger other countries to charge American diplomats tuition for their children."

"There are a lot of Australians who live in the suburds," said State Department legal adviser Horace Shamwell Jr. "If they have to pay tuition for their kids there might be recpocity involved."

The school board voted, 5 to 0, early yesterday to charge for the education of the approximately 2,000 students whose education has hitherto been effectively subsidized by taxpayers of the county and the state. The board, which has been under pressure from the Montgomery County Taxpayers League to pass the measure, used as its rationale that foreign government employes have been exempt from paying the state and local taxes that support the school system.School board members also have said that foreign government employes should pay nonresident tuition fees because their "permanent domiciles" are in other countries rather than in the county.

The taxpayers league has pointed to the presence of diplomats' children in county schools as a prime example of government waste.

School officials estimate the savings to the taxpayers at $3 million although the taxpayers league has estimated that the school system could save $15 million as a result of the measure.

The tuition charges for students whose parents pay neither property taxes nor U.S. income taxes will be $2,258 for students in grades one through six; $2,419 for students in junior high and high school, and $5,409 for handicapped students in special education classes.

Ambassadors are the only foreign government officials who can live in tax-exempt property, so only they will be billed for full tuition.

Diplomats and other foreign government employes, who do not pay income taxes but do pay property taxes, would be charged about half the tuition fee.