Israeli military personnel set up roadblocks and increased security throughout communities in the area, Ynetnews.com reported.
A 7-year-old boy was slightly injured in the attack at Bat Ayin in Gush Etzion and transported to a Jerusalem hospital, officials said. A passerby wrestled the ax away from the man before the attacker fled, police said.
Police said witnesses reported the attacker was acting wildly and attacked passersby before fleeing the area.
Gush Etzion Regional Council Mayor Shaul Goldstein said Bat Ayin's security squad shot at the man, but he managed to escape.
"The terrorist came in with an ax and injured two boys from Bat Ayin," Goldstein said.
No group claimed responsibility, The Jerusalem Post reported.
A Kadima lawmaker in the area at the time of the attack urged the Palestinian Authority to cooperate with Israeli forces to help catch the attacker.
"The first, most important thing is to find the murderer," Gideon Ezra said. "We must call on the Palestinian Authority to help catch this murderer."