Yusuf Abu Matar, 33, who also belonged to the Palestinian police force, died in a local hospital on Sunday.
An explosive device reportedly went off as he sat in his car in the Rafah refugee camp on the southern edge of Gaza, near the border with Egypt.
Palestinian security sources said they were investigating whether Matar's car had been booby-trapped, which could make him the victim of a targeted attack, or whether he had been carrying a bomb that exploded prematurely.
The Israeli army had no immediate comment on the incident.
Israel has often killed leaders of resistance groups in targeted strikes staged in Gaza, including members of Islamic Jihad. The organisation has killed dozens of Israelis in bomb attacks.
But Israel has apparently held off launching such strikes in recent weeks as new Palestinian Prime Minister Ahmad Quraya seeks to negotiate a truce with armed resistance groups and restart peace talks with Israel.
Elsewhere, the Israeli army imposed a curfew on a Palestinian area of the northern West Bank after one of its vehicles came under fire.
No one was hurt in the attack in the al-Labad area east of the town of Tulkaram, Israeli forces said, adding a search was underway for the attackers.