Violent demonstrations swept across the occupied West Bank today in reaction to the closing of an Arab university. Two Israeli soldiers and one Palestinian woman were injured, and at least 12 Palestinians were arrested.

During a rock-throwing demonstration in Nablus, Israeli soldiers opened fire, and a 50-year-old Arab woman, who was not involved in the demonstration, was wounded. Two Israeli soldiers were injured when their jeep was pelted with rocks outside the Kalandia refugee camp just north of Jerusalem.

Security forces used tear gas and fired rifles in the air to break up demonstrations in Ramallah, El Biera, Beit Jala and several other West Bank towns as troops sealed off the areas of disturbances and refused to allow reporters to pass roadblocks.

The Arab municipalities and trade unions called for a general strike Thursday both in the West Bank and Gaza, and security forces were put on alert for more demonstrations.

The disturbances were sparked by yesterday's closing for two months of Ramallah's Bir Zeit University, a center of Palestinian nationalism. The university, one of four Palestinian colleges on the West Bank, had been reopened only six weeks ago after a previous three-month shutdown.

The new closure stemmed from an incident Monday when an education official of the occupation government was chased off the campus by an angry crowd of Palestinian students after he had met with the university's vice president, Gabi Baramki.

Palestinian sources in Nablus said Israeli troops opened fire on demonstrators in the center of town about 11 a.m. today, injuring Amneh Ali Turki Anani, 50, in the head.

A spokesman for the Army command in Tel Aviv, however, said that two soldiers fired in the air when their vehicle was stoned, and that the woman was slightly injured by the ricochet as she watched from the top floor of a nearby building.

In central Ramallah, where the largest disturbances occurred, students chanting nationalist slogans were dispersed by tear gas and warning shots, and about a dozen were arrested. Three public schools in the town were closed because students did not show up for classes.

Ramallah Palestinians complained that for the second day, Rabbi Meir Kahane, American-born militant leader of the Jewish Defense League, appeared in uniform and with a weapon in the town square while serving on reserve security duty.

Kahane, whose militant Kach movement in Israel openly advocates the expulsion of all Arabs from the West Bank, was sentenced to nine months in prison by a military court in 1980 as a result of a series of disturbances in the West Bank involving Kach vigilantes.

Kahane was banned from entering Ramallah, but in April 1980 he was arrested again after he evaded an Army roadblock and distributed leaflets in Ramallah urging the residents to emigrate from the West Bank to Arab countries. Later the same year he was placed under administrative detention for three months on a charge of planning vigilante actions against Arabs.

An Army command spokesman said today that Kahane, who lives in the Kiryat Arba settlement near Hebron, had been routinely called up for annual reserve duty.

"Like any civilian called to reserve duty, he was posted with his unit, and it happened to be in Ramallah," an Army spokesman said.