The strike was the first since early July, when Israel responded to rocket fire from Gaza launched after its deadliest Israeli raid in the occupied West Bank in years.
The army said it hit "a military post belonging to the Hamas terrorist organisation in the northern Gaza Strip."
A military spokesman said the air strike hit an area where Palestinians had gathered earlier Friday, near the permanently closed Karni crossing.
A security source in the Palestinian territory told AFP that Israel "bombed a resistance observation post east of Gaza City," requesting anonymity as he was not authorised to speak publicly to the media.
There were no immediate reports of injuries resulting from the air strike.
Earlier Friday, an AFP journalist at the protest saw Palestinians throwing rocks and explosives towards Israeli forces, across the frontier, and two demonstrators with gunshot wounds.
Plumes of black smoke filled the area after Palestinians set tyres ablaze.
Twelve Gazans were wounded at various rallies along the border, the territory's health ministry said.
The Israeli military said "several explosive devices and grenades" were hurled at soldiers, none of whom were hurt.
The air strike comes after an explosion killed at least five Gazans during a border rally on Wednesday.
A bomb which may have been a hand grenade detonated while being carried by a protester, a witness told AFP on condition of anonymity.
Islamist militant group Hamas seized control of Gaza in 2007 and Israel has since imposed a crippling blockade.
There have been multiple wars fought between Gaza-based militants and Israel in recent years.
At least 34 Palestinians and one Israeli were killed in five days of cross-border exchanges in May.
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