A Hamas militant is reported to have been wounded in the air strike in southern Gaza.
Israeli troops also entered the Strip following the bomb attack, and one Palestinian was killed, medics said.
It is the worst violence since Israel's offensive against Hamas in Gaza ended with both sides declaring ceasefires.
No group has said it carried out Tuesday's bomb attack on an Israeli patrol near the border crossing of Kissufim.
One Israeli officer was badly wounded in the explosion and the other soldiers were lightly wounded, an army spokesman said.
Palestinian residents of Kissufim said they could hear Israeli helicopters circling overhead and the sound of heavy gunfire.
Medics in Gaza said a Palestinian farmer was killed by gunfire.
The Associated Press news agency quotes Hamas as saying one of its members was wounded in the subsequent air strike in the town of Khan Younis near Rafah.
Other reports say two people were wounded in the strike.
The violence comes as US President Barack Obama's Middle East envoy, George Mitchell, arrives in the region to seek a more permanent truce.
Israel has closed border crossings into Gaza because of the attack on the patrol, Israeli officials said, stopping the flow of aid supplies to Gaza's 1.5 million residents.
Aid agencies have been struggling to meet the urgent needs of tens of thousands of displaced, homeless and injured people in Gaza.