Moslem Druze militiamen took three Lebanese Cabinet ministers hostage today after Druze artillery shells rained on the airport, U.S. Marine positions and areas close to the Lebanese Defense Ministry and the presidential palace.

The three ministers were seized when they attempted to enter a Druze area south of the capital in an effort to meet with a Druze religious leader to put an end to the assaults, according to the state television.

Reuter quoted government officials negotiating for release of the ministers as saying the kidnapers demanded resignation of the Cabinet and removal of Lebanese Army troops from the Druze area.

The heavy mortar and artillery attacks on the fragile symbols of national authority were an outgrowth of a Druze offensive--in which four persons were killed--against a newly reinforced Lebanese Army position in the strife-torn hills south of the capital. It appeared designed to demonstrate the lengths to which the Druze will press their demands for more power in the Christian-led government and their will to resist further Lebanese Army deployment in the hills.

Beirut, already shaken by recent car bombings elsewhere in Lebanon in which scores of civilians were killed, reacted with alarm to today's attacks. Downtown streets were virtually deserted by late afternoon, and many shops closed as people hurried home.

Lebanese Army spokesmen acknowledged that Druze fighters had overrun several of their advance positions in the ground battles in the mountains, forcing the Army into what one described as a "tactical retreat."

At least three Lebanese women and a child were killed in the shelling in the capital and more than 30 others were wounded. Several draftees were wounded when shells fell near their basic training camp across from the Defense Ministry.

One U.S. Marine lieutenant sustained minor shrapnel wounds in the barrages that crashed near marine perimeter positions around the airport and the nearby headquarters for the 1,200-man marine contingent in the multinational peace-keeping force here.

Israeli radio said one Israeli soldier was killed and five wounded in the Israeli-occupied central mountains.

Robert C. McFarlane, President Reagan's new Middle East envoy, visited the marines in the early afternoon after a midday lull in the shelling. It then resumed and McFarlane left--a bodyguard shielding him as the car speedily drove off.

The Lebanese government shut down the airport this morning, diverting incoming traffic to airports in nearby countries, after the shells began to fall. It reopened briefly late in the morning to allow the departure of two fully loaded planes that had been trapped on the tarmac.

Prime Minister Shafiq Wazzan, who came out to speak to reporters during an emergency Cabinet meeting, termed the shelling a "national disaster." He indicated that the Army had been given orders to respond by firing on Druze military positions.

At the Cabinet meeting, three ministers--Adel Hamiyeh, a Druze who is finance minister, Public Works Minister Pierre Khoury, a Christian, and Shiite Moslem Adnan Mroue, who is minister of labor and health--reportedly volunteered to go to the heavily defended Druze areas south of the capital to meet with Druze Sheik Mohammed Shaqra. On their way, they were detained by gunmen in the Druzes' leftist Popular Socialist Party militia, according to state television.

The state radio later said the three ministers were "safe" in party leader Walid Jumblatt's palace in the town of Moukhtara, a mile from the place where they were seized. Jumblatt was reported to be out of the country.

The Druze are a breakaway Moslem sect that believes in reincarnation and considers the central mountains around Beirut as its sanctuary for customs dating back to Ottoman times. Druze also are found in Syria and Israel. While they wield influence in Israel, their political role in Lebanon is considered disproportionate to their 10 percent of the population.

Druze religious and political leaders or their surrogates have been conducting inconclusive negotiations with President Amin Gemayel and his advisers for the past couple of months over Druze demands for more power in the government.

The planned Israeli pullback from the mountains overlooking Beirut prompted the discussions. Both Druze and Christians live in the hills. Their militias, in a continuation of battles and feuds going back more than a century, have been fighting off-and-on this time since last August. Although the Israelis have been accused by both sides of alternately favoring one side or another, they have attempted to mediate. The disputes have involved shellings, kidnapings and murders of civilians.

The Druze have indicated that they fear that when the Lebanese Army comes to the mountains after the Israelis leave, the Christian-led Gemayel government will use the situation against them. They have demanded, as insurance, special arrangements and a reshuffling of power before the Army's deployment.

Gemayel and his advisers have said they would discuss security arrangements but have refused to enter into any negotiations for constitutional revisions, stalemating the talks.

The dispute has been exacerbated by the strong personal enmity between Gemayel and Jumblatt, both scions of families long in bitter conflict. The president's father, Pierre Gemayel, head of the ruling Christian Phalange Party, said of today's events: "If there shall be war, let it be and let the stronger people win."

Gemayel has said that if no agreement with the Druze is reached before the Israelis leave, he will deploy the Army in the troubled areas anyway. But last month, when three jeeploads of Army officers went to a Druze mountain village on a reconnaissance mission, hundreds of local residents poured onto the streets to protest. This spurred clashes that ended with the death of some villagers and injury of some of the military men.

Later last month, when Gemayel visited Washington, Druze militia shelled the airport, forcing its temporary closing in what has widely regarded here as a calculated effort to embarrass the beleaguered president.

Today's conflagration apparently was triggered by the government's decision to reinforce with armor, recoilless rifles, bedding and tents an Army redoubt around the village of Kfar Matta, about 10 miles south of Beirut. The government has said the military post, which is an anomaly because of its location in Israeli-held territory, was established last November at the request of Druze and Christian villagers on either side of it.

The Army described the 50-vehicle convoy that traveled through an Israeli checkpoint and up through Christian villages to the post as a normal rotation of men and equipment. But Druze said they saw it as a prelude to Army deployment in the mountains.

Before daybreak today, the Druze began their attack, first shelling the port and then the airport.

Army spokesmen said their guns at Kfar Matta were unable to reach the Druze artillery positions farther up in the mountains and that the Army initially was unable to return fire.

Some of the shells fired this morning landed in Shiite Moslem shantytowns near the airport, killing one woman motorist, another woman in her bed and another outdoors near a bakery. A small boy walking to school was also killed.

Other artillery rounds fell as close as 15 yards from marine positions and near Israeli positions.

Foreign military aides reported seeing Lebanese Army soldiers later in the morning looking for a place to set up their cannons. They ended up putting them near positions of the U.S. Marines and the Italian contingent in the multinational force.

When the Army began firing the heavy guns, the Druze in the mountains responded with the barrages near the Defense Ministry, presidential palace and the shell that landed about 500 yards from marine headquarters as McFarlane was visiting.