Palestinian medical staff said they could not reach the village as a result of the continuing violence.
Tensions in Bat Ayin and the surrounding Arab villages have been high since Thursday, when an unidentified Palestinian carrying an axe killed a 13-year-old boy.
Another boy, aged seven, was wounded in the attack, after which the Palestinian fled the scene. He has not been caught.
Bat Ayin, which lies near the Palestinian towns of Hebron and Bethlehem, is home to about 1,000 Israeli settlers.
Three people from the settlement were sentenced in 2002 by an Israeli court to prison terms ranging from 12 to 15 years for trying to set off a bomb near a Palestinian girls' school in Arab East Jerusalem.
The seven-year-old boy injured in last Thursday's axe attack is a son of one of the three jailed settlers.
The incident in Safa comes amid a general closure of the West Bank by Israel, in the run up to the Jewish holiday of Passover (Pesach).
Israeli security forces will be on high alert over the holiday period, an Israeli army spokesperson said on Tuesday. The closure will run until April 18.
Palestinians are denied entry from the West Bank during public and religious holidays because Israel considers its Jewish population to be at a high risk of attacks by Palestinian armed groups.
But the closures will also affect the ability of Palestinians who have jobs in Israel to reach their place of work, upsetting their livelihoods.
The annual Passover closure, on top of permanent checkpoint restrictions, is seen by many Palestinians and international observers as collective punishment of the Palestinian population.
Jews in Israel and around the world celebrate Passover in memory of the exodus of the Jewish people from slavery in Egypt in ancient times.