The shooting incidents took place near a flashpoint religious shrine known to Muslims as the Ibrahimi Mosque and to Jews as the Cave of the Patriarchs in late 2015 and early 2016.
They occurred amid a wave of Palestinian attacks targeting Israelis, but most of the assaults have been stabbings.
The two arrested were Nazar Fizel Mohamed Badie, 23 and alleged to be an operative of the Islamist movement Hamas, and his brother, Akram Fizel Mohamed Badie, 33.
Nazar Badie is accused of firing a homemade rifle from his family's home at civilians near the shrine on November 6. Two people were wounded, one of them seriously.
On January 3, Akram Badie allegedly fired on a group of soldiers near the shrine and seriously wounded a soldier.
On the same day, the two brothers are accused of firing on an army checkpoint in southern Hebron, lightly wounding a soldier.
Hebron, the largest city in the West Bank, has long been a source of tensions, with several hundred Israeli settlers living in the heart of the city under heavy military guard among around 200,000 Palestinians.
A wave of violence in Israel and the Palestinian territories since October has killed 177 Palestinians as well as 28 Israelis, an American, a Sudanese and an Eritrean, according to an AFP toll.
Most of the Palestinians who died in the violence were killed by Israeli forces while carrying out knife, gun and car-ramming attacks, according to Israeli authorities.
Others were shot dead by Israeli forces during clashes and demonstrations.
