The killing of at least three - and probably five - Israeli soldiers who were sightseeing and picking fruit in Arab orchards south of Tyre during an unauthorized jaunt into southern Lebanon Wednesday has touched off a full scale army investigation and some arrests.

One senior officer has been removed from his duties pending the outcome of the investigation, and a subordinate officer has been arrested. One of the two survivors of the incident, a civilian who was in southern Lebanon illegally, has also been arrested.

The Israeli chief of staff, Lt. Gen. Mordechai Gur, has placed southern Lebanon off limits to all civilians and all unauthorized army personnel.

The incident, which might easily have upset the fragile cease-fire in southern Lebanon, dramatized what many Israelis view as an unpardonable lack of discipline: soldiers taking their girlfriends into the newly-capture territory of southern lebanon, Israeli civilians casually picnicking near the ruins of bombed buildings, and buses of tourists being allowed to approach the border in the northern Israeli town of Metulla, even with the town under intermitten rocket attack.

Before the Israeli invasion, when the civil war still spurttered on in southern Lebanon, busloads of United Jewish Appeal travelers were taken to the northern border, and last summer, before a stop was put to that practice, tourists were allowed to wait by the border crossing to catch a glimpse of wounded Lebanese being brought across the frontier for medical attention.

Although all the details of the Wednesday incident are not known, the following account was pieced together from official army reports and newspaper accounts.

An Israeli Army sergeant and a private set out from Israel into Lebanon in a van in order to check on a tractor that had been left near the Lebanese village of Bint Jbail. On the way, they picked up foru hitchhicking army reservists who apparently had no authorization to be in Lebanon. Later they picked up a civilian who was in Lebanon illegally and, according to some reports, dressed in an army uniform which he was not authorized to wear.

The civilian had some maps and offered to take the group sightseeing. They passed through the town of Joya, which was heavily damaged by Israeli bombing and shelling during the invasion last month, and apparently they thought they could take a shortcut down the coast road to Israel without having a backtrack through Bint Jbail.

They managed to pass through the last checkpoint marking the end of Israeli military control, beyond wich lay Tyre and the Palestinians. It is not clear how they were allowed to pass, or if they talked their way through the last checkpoint, and this is one of the primary matters under investigation.

After passing into hostile territory, the group apparently saw an orchard and stopped to pick some of the fruit. There they encountered some Arab children and soon afterward two armed Palestinians appeared and ordered the Israelis to go with them.

Other Palestinians appeared. The Israeli started to argue with them, and one of the Palestinians fired a warning shot in the air. Some of the Israeli were armed with submachine guns, but it is not clear whether they opened fire.

The sergeant, who was driving, tried to make a break for it, and almost immediately the van was hit by automatic weapons fire and by a rocket. Three Israelis were killed outright, but the sergeant managed to keep the vehicle going until he swerved off the road to avoid an oncoming car. Since the van was stuck in the sand, the remaining four, all of them wounded, ran away.

The sergeant, who had been wounded in the back, said he was out of breath and could not continue. The others left him - apparently breaking one of the strictist codes of the Israeli Army, which is to never leave a wounded conrade behind.

Darkness was falling. Another of the men dropped behind, and only two - a soldier and the civilian - made it back to Israeli lines. The soldier is now in a Haifa hospital, and the civilian, who was lightly wounded, is under arrest.

The Israeli Army, about 100 u.n. soldiers and the Palestinians, too, spent a good part of the night looking for the men. It was feared that some of the Israeli had been captured but, according to International Red Cross sources, the Palestinians have now said they have all five bodies.

Some Arab radio reports have said that the seven were part of an Israeli reconnaissance group, but the official army account disputes that version, and the subsequent investigation and recriminations have convinced many Israelis that the victims died in a wasteful and useless tragedy that should have been prevented.