Emergency services chief Ashraf al-Qudra told AFP that Musaad Alzaneen, a man in his early 20s, was killed in the raid on farmland near the town of Beit Hanoun.
He later added that Sharif Nasser, aged 31, had died of injuries sustained in the attack.
The Israeli military spokesperson's office said the target was a Palestinian "rocket-launching squad".
"Israel Air Force aircraft targeted terrorists preparing to launch rockets in the northern Gaza Strip," it said in a statement.
"The mission was carried out in order to eliminate an imminent attack targeting civilian communities of southern Israel."
Israeli media had earlier reported a failed rocket attack, with the projectile apparently falling short and landing within the Gaza Strip.
On Friday an Israeli air strike destroyed a rocket launch site in Gaza which also represented "an imminent threat," the army said at the time.
No casualties were reported in the attack.
Tensions have risen in and around Gaza after a year of relative calm.
An increase in Israeli raids and Palestinian rocket attacks as well as border incidents in the past few weeks have raised the possibility of a major new confrontation between Israel and Hamas.
Monday's strike occurred as Israeli Prime Minister Benjamin Netanyahu met US President Barack Obama to discuss the future of the peace process with the Palestinians.
Hamas, the Islamist movement that ousted the Western-backed Palestinian Authority from Gaza in 2007, opposes a peace deal.