"This is the only barrier of its kind in the world, which will effectively block the possibility of infiltrating into Israel by sea", Defense Minister Avigdor Lieberman said in a statement on Sunday. Since then, Israeli forces have killed at least 124 Palestinians and injured thousands more.
Israel's military confirmed that it targeted an observation post, calling the attack retaliation for a bomb that had been placed next to the border fence overnight.
"We will not give up our duty to the blood of the martyrs shed by the occupation, and we know how to respond to this risky escalation", Islamic Jihad said in a statement.
Separately on Saturday night, Israeli aircraft struck two targets belonging to Hamas, but there were no reports of casualties.
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It said troops responded with tear gas and live fire.
No Israelis have been killed in the clashes.
Around 5,000 Palestinians had turned out for protests against Israeli forces on Friday, the smallest number since the six-week-long "Great March of Return" protests kicked off on March 30 demanding the right to return to ancestral homelands in what is now Israel.
Low-level demonstrations along the border have continued since protests peaked on May 14, when at least 61 Palestinians died as tens of thousands of Gazans protested the USA moving its embassy from Tel Aviv to Jerusalem.
Israeli authorities are also constructing an underground barrier beneath the Gaza-Israel boundary to stop Hamas from digging tunnels into Israeli territory.
According to Israeli media, the defence ministry ordered the construction of the barrier in the aftermath of the 2014 war with Gaza and after discovering that Hamas fighters had successfully entered Israel by sea.