“Three Grad rockets were fired at Jewish positions in occupied Palestine,” the group said in a statement posted on Twitter by supporters.
Israeli police said earlier they had found rocket remnants in an open area. No damage or casualties resulted.
“Yes, the rocket was fired from Sinai,” an Israeli military source said, confirming an Israeli Army Radio report that the missile was launched from the desert region bordering Israel and Gaza.
It was possible the launch was linked to the fighting in Sinai, the military source said.
Militants of the Sinai Province group launched their biggest assault in years against Egyptian security forces on Wednesday. Dozens of people have been killed in the past few days of clashes.
The Israeli military on Friday closed a southern highway, part of which runs along the Egyptian border, as a safety precaution.
Egyptian security sources told Reuters they were investigating the reports and said there was no immediate evidence a rocket was launched from Egyptian territory.
Militants have in the past fired rockets from Sinai into Israel.
Israel has accused Hamas, the Islamist group which controls Gaza, of helping Islamic State in Sinai, an allegation Hamas, denies.