The group, Islamic Jihad, denied the Israeli allegation. It had previously threatened reprisals should one of its activists in Israeli detention, Mohammed Allan, die of a hunger strike. Allan ended the fast on Wednesday after an Israeli court intervened.
Israeli officials said two rockets struck close to a northern village in the upper Galilee, near the Lebanese border, setting off brush fires but causing no casualties. Air-raid sirens had sent residents to shelters.
The attack was unusual as that frontier had been largely quiet since the 2006 war between Israel and the Lebanese guerrilla group Hezbollah. By contrast, the Israeli-occupied Golan, about 16 km (10 miles) to the east, has occasionally come under fire from within Syria during the four-year-old civil war there.
The Israeli military said in a statement the rockets that hit the upper Galilee "were launched from the Syrian Golan Heights ... by Islamic Jihad, sponsored by Iran".
Israel "holds the Syrian government responsible for attacks emanating from Syria", the army said, adding it had retaliated against targets in Syria.
An Israeli military source said the air force and artillery had struck "five or six times" in the Syrian Golan.
Syrian state TV confirmed Israeli strikes had hit, but said only material damage was done after "several missiles" targeted a transportation centre and a public building in the Quneitra area near the Israeli frontier.
Rebel sources in Syria, however, said the strikes hit some of Damascus's military facilities on the Golan. A monitor initially reported casualties but did not elaborate.
Islamic Jihad's leaders are based in the Syrian capital and most of its followers are in the Gaza Strip, whose dominant faction Hamas has mostly been observing a truce with Israel that ended the war in the Palestinian enclave a year ago.
Dawoud Shehab, an Islamic Jihad spokesman in Gaza, denied the group had fired on Israel from the Syrian Golan.
"Israel is trying to divert attention from the defeat that it suffered in the face of the determination of the hero prisoner, Mohammed Allan," Shehab told Reuters.
Allan had refused food in protest at being detained without trial by Israel. On Wednesday, he called off the 65-day hunger strike after Israel's top court suspended his arrest warrant.
The possibility that Allan might die of his fast had drawn Islamic Jihad threats to attack Israel, which in turn deployed Iron Dome rocket interceptors outside Gaza as a precaution.
Islamic Jihad acknowledges receiving support from Iran, Israel's arch-foe. Israel has sought to highlight such Iranian backing for regional armed groups as it campaigns against U.S. congressional approval of the July 14 deal curbing Tehran's nuclear programme in exchange for international sanctions relief.
Israel captured the western Golan in the 1967 Middle East war and annexed it, a move not recognised abroad. While saying it is keeping out of the Syrian civil war and that some of the shooting against its side of the Golan has been stray fire, Israel has usually retaliated against Damascus's assets over the armistice line.
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