"Fighter jets, military helicopters and tanks targetted Hamas positions in the Gaza Strip," including "the navel defence system used by Hamas, underground infrastructure and observation posts," the Israeli army said in a statement, specifying that this was a response to the balloon bombs.
The Palestinian Red Crescent said that a pregnant woman and a three-year-old child were injured in the attacks and taken to hospital.
The attacks come a day after the announcement of a deal to normalise relations between Israeli and the United Arab Emirates that has been denounced by the Palestinians, including Hamas.
Read also: 'Deal of shame': UAE formally endorses Israel's occupation of Palestine
Dozens of blazes have been reported this week in southern Israel, as makeshift firebombs attached to bunches of balloons or kites set agricultural fields and scrubland alight.
In response, Israel has closed its cargo crossing with Gaza and also reduced the territory's permitted coastal fishing zone.
Friday's attacks on sites used by Hamas were the sixth such night-time operation this week.
Hamas on Thursday condemned Israel's attacks on Gaza and its sanctions as "dangerous and aggressive behaviour", warning of "consequences" the Jewish state will bear.
Islamist group Hamas, which controls the Gaza Strip, has fought three wars against Israel since 2008.
Despite a truce last year backed by the UN, Egypt and Qatar, the two sides clash sporadically with rockets, mortar fire or incendiary balloons.
The Gaza Strip has a population of two million, more than half of whom live in poverty, according to the World Bank.
Palestinian analysts say fire from Gaza often aims to pressure Israel to give the green light for the transfer of Qatari financial aid into the strip.
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