In a move the State Department says may set an ominious precedent for U.S.-Arab relations, Kuwait has refused to accept a veteran diplomat, Brandon W. Grove Jr., as U.S. ambassador because he served as American consul-general in Jerusalem.

The State Department yesterday refused to comment, but some officials confirmed that they were shocked last week when Kuwait, regarded as a moderate Arab state friendly to the United States, rejected Grove as a prospective envoy.

According to the officials, the matter is regarded here as very serious and delicate because it could encourage other Arab governments to interfere with the assignment of U.S. diplomats in the Middle East by ruling the Arab world off-limits to those who have served in Israel.

Israel and its supporters have charged frequently that the State Department's Bureau of Near Eastern and South Asian Affairs has an anti-Israeli bias because almost all its members have spent most of their careers in Arab countries and tend to view Middle East conflicts from an Arab perspective.

The department has tried to counter that objection by ensuring that a number of career officers specializing in the Middle East get first-hand experience in Israel. If the Kuwaiti action becomes a precedent, the officials said, there is a danger that Israel will become a "diplomatic ghetto," where diplomats are unwilling to serve because of possible limitations that would put on their future assignments.

They also said there is concern within the State Department that Kuwait's action might be part of a move by Persian Gulf oil-producing states, which look to Saudi Arabia for foreign-policy leadership, to distance themselves from the United States and move closer to Syria and its resistance to U.S. efforts to get foreign forces out of Lebanon.

The Reagan administration is known to be concerned about the almost ostentatious reserve the Saudis have displayed toward the United States in recent weeks.

In May, the Saudis encouraged Secretary of State George P. Shultz to believe they supported the Israeli-Lebanon peace agreement and would work to win Syrian cooperation for a joint withdrawal of Israeli and Syrian forces from Lebanon. But, as Syria's opposition grew more intense, the Saudis backed away.

President Reagan's new special Middle East envoy, Robert C. McFarlane, received a very cool reception in Saudi Arabia last week. The Saudis, without mentioning Syria, told McFarlane only that Israel must withdraw from Lebanon.

The officials said it still is too early to tell whether the Kuwaiti action is a further reflection of this trend among the gulf states. But, they added, the State Department is at a loss to explain why Kuwait rejected Grove.

There have been problems in the past with attempts to assign Jewish-American diplomats to Arab countries. However, Grove is not Jewish, and officials were unable to recall past instances when an Arab government has blocked assignment of an American diplomat because he had served in Israel.

They added that the situation is especially puzzling because Grove was somewhat controversial, from the Israeli point of view, during his recently completed three-year assignment in Jerusalem.

Since the United States does not recognize Jerusalem as Israel's capital, the consulate general is separate from the U.S. Embassy in Tel Aviv, and its principal function is to maintain contact with the Palestinians on the Israeli-occupied West Bank.

For that reason, the consulate general is regarded by many Israelis as a center of pro-Palestinian attitudes. Grove, together with previous holders of the consul general's post, was criticized frequently in Israel for allegedly being an opponent of Israel's West Bank policy.

Grove, 54, also does not have an extensive background in Middle East affairs. For much of his diplomatic career he has been involved with German and European affairs. And, before going to Jerusalem, he served as a deputy assistant secretary for Latin America.

His assignment to Kuwait was part of the reshuffle of major U.S. ambassadorial posts now under way in the Middle East. Officials said that the administration is weighing possible other assignments for Grove and has not decided what to do about filling the vacancy in Kuwait.