Sam Fahd Abu Haikal was killed on Friday evening, and his parents were wounded while driving in the Tel Rumeida area south of Hebron City, according to the ministry.
The official Palestinian news agency WAFA said the infant was critically wounded after being struck in the face by the same bullet that injured his mother.
He later died of his injuries.
His father, Fahd Abu Haikal, a lecturer at Bethlehem University, was shot in the hand.
They were travelling from Bethlehem to visit family in Hebron when soldiers opened fire, the agency reported.
Israel's military has scaled up military operations in the West Bank since the October 7, 2023, Hamas attack that killed some 1200 people and took 251 people hostage, which triggered the war in Gaza.
Israel's retaliatory military campaign has killed more than 72,900 Palestinians, according to Gaza's health ministry.
The United Nations said in May that more than 1000 Palestinians had been killed in the West Bank and east Jerusalem since the war began, at least 240 of them children.
Forty-nine people had been killed since the start of 2026, it said.
The Israeli military said on Friday an initial inquiry found that the injured were uninvolved civilians and said the situation is under review.
It also said soldiers shot at a vehicle that was perceived to be accelerating toward them in the Hebron area.
It said soldiers responded with single shots, wounding three Palestinians who were evacuated for medical treatment.
At Al-Ahly Hospital in Hebron, the baby's father told Associated Press reporters that a bullet struck the car's windshield before piercing his hand, then his son and wife.
"It entered the child's face on the right side and exited on the left, then passed directly into his mother's face and exited on the other side, with shrapnel lodged near her heart," Abu Haikal said.
The mother is in critical condition because there was shrapnel close to her heart, he said.
They have not told her yet that her son, who turned seven months old on Friday, was killed.
The baby's grandmother, Feryal Abu Heikal, was in the car during the shooting and said they were driving near a checkpoint and stopped when they saw Israeli military vehicles and soldiers in the distance.
As the forces fired at them, she initially thought it was warning shots before they were struck, she said.
"The scene was horrific to see a seven-month-old baby with a smashed face," she said.
"What kind of army in the world does this? ... What happened to my grandson can't be easily forgotten."
The infant's funeral is expected later on Saturday.
In March, Israeli soldiers fired on a car carrying a family in the northern West Bank, killing four people, including two children, the Palestinian Authority's health ministry said at the time.
Israeli soldiers accused of harming Palestinians are rarely penalised and were indicted in fewer than one per cent of cases based on 2427 complaints alleging wrongdoing between 2016 and 2024, according to Israeli rights group Yesh Din.
More than 700,000 Israelis live in the occupied West Bank and east Jerusalem, territories captured by Israel in 1967 from Jordan and sought by the Palestinians for a future state.
11°C