"A terrorist opened fire at a family driving on route 60, near Al Fawar, south of Hebron," the army said in a statement.
"As a result, the vehicle crashed, killing one passenger and wounding three more," it said.
The army said troops were "searching the area for the gunman who fled the scene".
Violence since October has killed at least 214 Palestinians, 34 Israelis, two Americans, an Eritrean and a Sudanese.
Others were killed in clashes with security forces or by Israeli air strikes on the Gaza Strip.
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