An Israeli military spokeswoman said he was targeted for "supervising commandos responsible for firing rockets at southern Israel".
A statement from the Al-Quds Brigades said: "The assassination of the general commander will open the door wide to a wave of martyrdom operations."
Huge explosion
His car was reported to be full of explosives and a huge explosion could be heard across the city. A second man was killed in this attack.
Hundreds of Islamic Jihad fighters gathered in the streets and fired into the air after the strike.
Hours later, a second Israeli attack killed four more Islamic Jihad fighters, including a rocket maker, on the streets of Gaza City, the group said.
Three of the men died immediately, while the fourth succumbed to wounds in hospital hours later.
An Israeli military spokeswoman said the attacks targeted fighters preparing to fire rockets at Israel.
Medical workers said the attacks also wounded two bystanders.
Third strike
A third air strike, also confirmed by the Israeli military, killed three Islamic Jihad fighters in a car near the northern town of Beit Lahiya, as they emerged from morning prayers, medics said.
Meanwhile, in the occupied West Bank, 25-year-old Tarek Abu Rali, a local commander of the Al-Quds Brigades, was killed by undercover Israeli troops as he drove in a car in the northern town of Jenin, medics and Islamic Jihad said.
Islamic Jihad acknowledged it had suffered heavy losses but said it would retaliate with suicide attacks inside Israel, threatening to unleash "a wave of martyrdom operations."
Thousands of Gazans took to the streets in funeral processions for the dead fighters, whose bodies and coffins were draped with black Islamic Jihad flags.
Matan Vilnai, Israel's deputy defence minister, hailed the "successes," saying the military was targeting the leadership of the group.
Speaking to the military's radio station, he said: "The important thing is not the number of them who are hit, but their place in the organisation's hierarchy."
Islamic Jihad claims responsibility for most of the rocket attacks from Gaza against Israel, although most of the projectiles fall without causing casualties.
Israel accused al-Harazeen of being one of the key leaders behind those attacks.
Palestinian officials said al-Harazeen, who had been on Israel's most wanted list for nine years, was the most senior commander to be killed in an Israeli strike in the Gaza Strip in more than a year.
Calls have grown in Israel over the past several months for the military to launch a widespread ground offensive in Gaza to put an end to the daily firing of rockets and mortars from the Hamas-run territory.
Most of the projectiles fall without causing casualties.