Mr Lieberman has in the past proposed laws that have angered Israeli Arabs
Israeli Foreign Minister Avigdor Lieberman has proposed a new regulation that would prevent most Israeli Arabs from becoming career diplomats.
It would exclude most Arab citizens, who do not serve in the army, as well as ultra-Orthodox Jews, who are exempted from conscription.
He said that only those who complete military or national service should be eligible for foreign ministry training.
Mr Lieberman said he would propose a law to parliament, if necessary.
Current Israeli law guarantees all citizens equal access to the civil service.
More than five Israeli Arabs, Muslims and Christians, currently work as diplomats in the foreign ministry, the Israeli Haaretz newspaper reported.
Mr Lieberman's proposal came at a foreign ministry administrative meeting.
Israeli Arabs, who make up about a fifth of Israel's population, roughly 1.45 million people, are of Palestinian Arab descent.
During the war that surrounded the creation of the state of Israel in 1948, hundreds of thousands of Arabs were forced from or fled their homes.
Those who remained within what became Israel, and their descendents, have been granted citizenship and are known as Israeli Arabs.
Israeli Arabs are citizens of Israel - although their "civic duty" differs as they are exempt from compulsory military service, although Druze and some Bedouin Arabs serve in the military.
But Israeli Arabs frequently describe themselves as "second-class citizens" and say they face institutional and social discrimination.
A programme of voluntary, non-military national service is open to all Israeli citizens, but has seen only limited participation from Israeli Arabs.
Mr Lieberman, a hard-line nationalist, has previously tried to sponsor laws requiring citizens to swear allegiance to Israel as a Jewish state and to ban the marking of the Nakba - the Palestinian "catastrophe" of 1948.
These measures have not been enacted, though laws stopping state funding for organisations and activities that reject the existence of Israel as a Jewish state have.