The missiles hit the home of Mariam Farhat, better known as Umm Nidal, a Hamas representative at the Legislative council on Wednesday.
The house is believed to belong to her son, a wanted member of the al-Qassam Brigades, Aljazeera's correspondent said.
No casualties were reported and residents were warned in advance of the raid - the second time that Israeli attacks have destroyed the Farhat family home.
An Israeli army spokeswoman said the air strike had targeted a weapons storage and manufacturing facility.
Farhat first won attention for appearing with her 17-year-old son Mohammed in a video recorded before he carried out a shooting attack on a Jewish settlement in 2000, in which he killed five people before being shot dead.
Israel has frequently carried out such strikes on buildings it says are used by militants, during a three-month-old Gaza offensive to try to recover a captured soldier and stop cross-border rocket fire.
Meanwhile, a Palestinian boy was shot dead by Israeli fire near the al-Ain refugee camp in Nablus when Israeli forces and Palestinian fighters exchanged fire.