The pre-dawn blast caused extensive damage at the home of Sheikh Hisham Salem, his Al-Sabirin group said in a statement.
Shiite Muslims are a tiny minority among Palestinians who are almost exclusively Sunni Muslims or Christians.
Al-Sabirin, which says it is supported by Iran, accused "the occupier (Israel) and its collaborators."
The Israeli army declined to comment on the allegations.
Reliable information is difficult to ascertain in Gaza, which is blockaded by Israel and Egypt and run by Islamist group Hamas.
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Shortly after the explosion, Gazan security forces went to the scene and opened an investigation to find the perpetrators, security sources said.
"We went out and found an explosive device placed near the door of the house," said a brother of the leader, Issam Salem, who was in the house at the time of the blast.
"The windows of the house and those of a bus were blown out," he told AFP, adding that the explosion had sent children inside the home into a panic.