Two other people were wounded, said Yeroham Mandola, a spokesman for the Israeli rescue services.
The attack on Negahot, a settlement near the city of Hebron, came after nightfall, when Israelis began marking Rosh Hashanah.
"We can see that terrorists quite often choose religious holidays to commit their murderous activities. We have had many warnings to this effect and the security forces of Israel are on high state of alert," said government spokesman Avi Pazner.
Israel has received more than 40 warnings about possible terrorist attacks over the two-day holiday, he said.
Israel radio reported the attacker appeared to have been a lone gunman who got through the fence of the isolated settlement.
The attacker invaded a house and began shooting, killing a 30-year-old Israeli man and the baby girl, according to the radio.
"To our regret, we have two killed and two more slightly wounded," said Dror Richter, spokesman for Israel's ambulance services.
The attacker was shot and killed by soldiers guarding the settlement, according to the radio.
Holiday celebrations across Israel were marked by heavy security, with thousands of officers deployed at synagogues, parks and intersections to try to prevent attacks by Palestinian militants.
Earlier in the week, Israel sealed off the West Bank and Gaza Strip for the duration of Rosh Hashanah, reports CBS News Correspondent Robert Berger.
The intention was to bar Palestinians from entering Israel until Monday. Israel imposed the measure anticipating possible attacks by Palestinian terrorists might trying to mar the holiday.
"There is no holiday feeling," said Avraham Diskuri, 32, a vendor at Jerusalem's Mahane Yehuda open air market. "With all that has happened, the attacks, all the children killed, it is not simple," he said. "It is going to be a lot worse, look at the security and the economic situation, it is only going to get worse."
"A page is about to be torn from the calendar, a year in which so many good people were torn away from us," said Rabbi Stewart Weiss, in a Rosh Hashanah prayer.
Also Friday, Israeli newspapers, citing Israeli officials reported that England and Germany are willing to release Iranian and Lebanese prisoners they hold, in exchange for information on missing Israeli airman Ron Arad, who Israel says is held by Iran.
Secretary of State Colin Powell planned to meet Friday with U.N. Secretary-General Kofi Annan, Russian Foreign Minister Igor Ivanov and Javier Solana, the European Union's foreign policy chief. The four form the group that produced the "road map" peace plan.
Powell intended to ask them to make clear to Arafat that he should "get out of the way" and cede authority to security officials who intend to dismantle terror groups that have killed hundreds of Israelis.
"We believe firmly in the concept of the road map," he said. "And it is still there."
Sharon told the Israeli daily Yediot Ahronot that Israel is determined to "remove" Palestinian leader Yasser Arafat one day. He said a decision to that effect by Israel's security Cabinet on Sept. 11 canceled his personal promise to President Bush — made several years ago — not to harm the Palestinian leader physically.
"You have to keep in mind that it is very difficult to ensure that he (Arafat) won't be harmed if we seize him," Sharon said.
Other top Israeli officials have said the term "removal" could mean both expulsion and assassination, but Sharon's remarks seemed to suggest that the first choice is to oust Arafat, not kill him.
Sharon said that American concerns will be taken into account. "But I repeat and emphasize: the fundamental decision to remove Arafat has been adopted by Israel," Sharon said.
The Cabinet decision was roundly condemned by the international community, including by the United Nations.
Israeli Foreign Minister Silvan Shalom told Powell this week that Israel did not plan to take action against Arafat right away, and would consult the United States before such a move, a U.S. State Department official said Thursday. The Bush administration has asked Israel not to exile him.
In the West Bank, the incoming Palestinian prime minister, Ahmed Qureia, said he has concluded consultations on his new Cabinet and will present the team of ministers to parliament for approval within the coming days.
Leaders of the ruling Fatah party will meet Saturday to discuss and approve the names, Palestinian officials said. One-third of the ministers will be newcomers from Fatah, and at least two Cabinet members, Foreign Minister Nabil Shaath and Finance Minister Salam Fayad, will keep their jobs, the officials said.
Qureia has given Fatah — and thereby Arafat — considerable say in putting together the Cabinet. Qureia has said that, unlike predecessor Mahmoud Abbas, he will not challenge Arafat. The United States had initially hoped that the new post of prime minister would help sideline Arafat by forcing him to give up some power.
Israel has said it would not deal with an Arafat-controlled Cabinet.
However, Sharon has not ruled out doing business with Qureia, whom he has met repeatedly in recent years. In an interview with Yediot, Sharon described Qureia as a cunning politician and said he would judge him on his deeds, not his statements. Israel wants the Palestinians to dismantle Palestinian militant groups, as required by the U.S.-backed "road map" peace plan, but Qureia has suggested he will not use force against the militants.