Iyad al-Bozum, an interior ministry spokesman in Hamas-ruled Gaza, said that gunmen opened fire on Faqha in the Tell al-Hama neighborhood, according to AFP.
"An investigation has been launched," he said, without providing further details.
Faqha was a senior Hamas official in Judea and Samaria but was transferred to Gaza after his release.
Faqha, according to the Hebrew-language Walla! news website, was behind many terrorist attacks against Israelis and was a senior member of the group’s so-called “military wing”.
He was originally sentenced in 2003 to nine life terms after being convicted of sending a terrorist to carry out a suicide bombing attack. The terrorist blew himself up on an Egged bus near the city of Tzfat, murdering nine people.
While it remains unclear who was behind his death, Hamas accused "agents of the occupation in the Gaza Strip" of being behind the shooting, according to Walla!.
The Islamic Jihad terrorist group blamed Israel for Faqha’s death and issued threats against the Jewish state.
"We warn Israel, a return to the assassination policy will change the confrontation and the response from the resistance in the Gaza Strip will be a difficult one," the group said.