Three of the 12 wounded were in serious condition, the military told AFP.
The armed wing of Palestinian militant group Hamas earlier claimed the rocket attack, which led Israeli authorities to close the crossing, used to deliver aid into Gaza.
The military said 14 rockets were fired at the crossing from an area adjacent to the Rafah crossing.
In response, the air force carried out a rapid response and destroyed the launchers from which the projectiles were fired, military spokesman Peter Lerner told journalists in an online briefing.
"It's a very serious event from our perspective, it's unacceptable, and the IDF (army) is investigating why the soldiers were killed as the siren was sounding," he said.
The army was "not aware of any interception that took place" during the incoming fire, he said.
"The airforce will look into exactly what happened," Lerner added.
The soldiers were hit while guarding heavy machinery, tanks and bulldozers that are stationed in the area.
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