The exchange came hours after two Palestinian teenagers were killed by Israeli fire during clashes on the Gaza border.
The overnight raid comes after PM Benjamin Netanyahu - who is aggressively campaigning for re-election after his failure to secure a coalition government - vowed a "vigorous response" to Hamas. The group fired five rockets into the occupied territories on Friday night, setting off sirens in Israeli settlements along the Gaza border as well as in the city of Sderot.
It "dropped what seems to be an explosive device" near the security fence, damaging a military vehicle before returning to Gaza.
The Israeli military frequently bombs the Gaza Strip, with civilians being the main target of such attacks.
Egypt has in the past helped broker unofficial ceasefires between Israel and Hamas. "Any attempt to harm our citizens and our soldiers will be met with a forceful response", Netanyahu said in a statement.
Three 13-year-olds crossed over from the southern Gaza Strip and a search revealed a knife, the army said in a statement.
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An Israeli military spokesman said troops guarding the border on Friday were faced with more than 6,000 demonstrators at several points along the fence, some hurling explosive devices and firebombs.
Around 210 Palestinians have been killed since the protests began in March 2018, Gaza medical officials say.
On Friday, Israeli forces shot dead two teenagers during regular weekend protests along the volatile fence.
Israel says any such return would mean its end as a Jewish state and accuses Gaza's Islamist rulers Hamas of using the protests as cover for attacks.
The protesters have been calling for Israel's siege of the coastal enclave to be lifted and the right of return for Palestinians to their ancestral homes in Israel from which their families were expelled in 1948.
Israel has also launched three major wars against the enclave since 2008, killing thousands of Gazans each time and shattering the impoverished territory's already poor infrastructure.