Israeli police spokesman Micky Rosenfeld said the incident occurred around midnight, when a man ran at a border police officer with a knife, prompting him to open fire.
His family says Anas and his brother were on their way back from Jericho when he was stopped at the military checkpoint near Bethlehem.
Israeli forces asked him to get out of the car, before shooting him dead, they say.
“The Israeli army assassinated Anas after they forced him to get out of the car,” his family told Ma’an.
Ismail, his brother, was wounded in the incident and is being treated for shock in al-Ahli hospital. He says that his brother was assaulted before being shot dead by Israeli forces.
Palestinian security sources told Ma’an that the military liaison office will form a committee to investigate al-Atrash’s death.
They will ask Israel to check footage from security cameras positioned at the checkpoint.
Thousands of people will attend al-Atrash’s funeral after Friday prayers in Hebron.
Hours earlier, Israeli forces shot and killed a Palestinian man at the Zaatara checkpoint in southern Nablus.
The 20-year-old man from Nablus was shooting fireworks at Israeli soldiers, who responded by shooting the Palestinian to death, witnesses said.