It was the worst violence between Israeli and Palestinians in the coastal enclave since a ceasefire was agreed last November at the end of an eight-day conflagration.
The Israeli military said its aircraft targeted a tunnel used by militants to facilitate attacks on Israelis and accused Hamas, Gaza's rulers, of breaching the terms of the ceasefire.
A Hamas source said three of its men were in the tunnel at the time of the attack and were killed in the blast.
Hours earlier, one Palestinian militant was killed and five Israeli soldiers wounded after violence broke out when Israeli forces detonated part of a separate tunnel they had recently uncovered stretching from Gaza into Israel.
Hamas has said it dug the tunnel, which was uncovered last month. Israel says the underground chamber ran for one mile and was intended to let militants cross deep beneath the border fence and carry out surprise attacks.
At a sermon before Friday prayers, senior Hamas leader Khalil Al-Hayya said the clash showed Hamas fighters were "alert and ready with their fingers on the trigger". He added: "We are not interested in an unjustified escalation but we have the right to defend our people."
The violence came at a difficult time for Hamas, which lost its most powerful backer in July when Egypt's Islamist President Mohamed Mursi was ousted by the military. Relations with Egypt have deteriorated sharply since then.
The head of Israel's southern command, Sami Turgeman, indicated Israel was not seeking an escalation in violence. He said: "Quiet will be answered with quiet. An attack will draw a painful response."
The Israel-Gaza frontier had been mostly peaceful for the past year following the Egyptian-brokered ceasefire.
The Palestinian Authority, Hamas's Western-backed rivals who exercise limited rule in the Israeli-occupied West Bank, resumed peace talks with Israel in July.
Tension has also mounted in the West Bank, where eight Palestinians have been shot dead by Israeli soldiers and three Israelis have been killed since the negotiations began.
Meanwhile, Israeli warplanes attacked a shipment of Russian missiles inside a Syrian Government stronghold.
It was a development that threatened to add another volatile layer to regional tensions from the Syrian civil war.
The revelation came as the government of President Bashar Assad met a key deadline in an ambitious plan to eliminate Syria's entire chemical weapons stockpile by mid-2014 and avoid international military action.
An Obama administration official confirmed the Israeli air strike, but provided no details. Another security official said the attack occurred late on Wednesday in the Syrian port city of Latakia and that the target was Russian-made SA-125 missiles.
Since the civil war in Syria began in March 2011 Israel has carefully avoided taking sides, but has struck shipments of missiles inside Syria at least twice this year.
The Syrian military, overstretched by the civil war, has not retaliated and it was not clear whether the embattled Syrian leader would choose to take action this time.
Mr Assad may decide to again let the Israeli attack slide, particularly when his army has the upper hand on the battlefield inside Syria.
Israel has repeatedly declared a series of red lines that could trigger Israeli military intervention, including the delivery of "game-changing" weapons to the Syrian-backed Lebanese Hezbollah group.
Israel has never officially confirmed taking action inside Syria,to avoid embarrassing Mr Assad and sparking a potential response.