Israeli media reported that the bus was hit by a mortar and that one Israeli man was seriously injured in the attack.
Its fighters gave chase as the vehicle sped away, it said.
Rocket-fire alarms were sounded in several locations near the Gaza Strip on Monday afternoon.
Israel's military said it was carrying out air strikes "throughout the Gaza Strip" in retaliation for the rockets, which came after an Israeli commando was killed in a botched raid in Hamas territory.
In the immediate aftermath of the clash, Israel said it identified 17 launches - likely rockets or mortars - toward its territory from Gaza, with three intercepted by missile defences.
The military wing of Gaza's ruling Hamas claimed responsibility for the barrage of rockets fired into southern Israel.
"The joint command of Palestinian factions announce the beginning of bombardments of the enemy's settlements with scores of rockets", the Ezzedine al Qassam Brigades group said in a statement.
Hamas said the Israeli actions dealt a blow to Egyptian, Qatari and United Nations efforts to broker a long-term ceasefire and ease an Israeli blockade that has deepened economic hardship in Gaza.
The flare-up was in response to an Israeli operation late on Sunday that appears to have gone awry, in which soldiers killed seven Hamas militants and lost a lieutenant colonel in an ensuing firefight.
Israeli gunfire has killed more than 220 Palestinians since the start of the demonstrations, which have included breaches of Israel's border fence.
Hamas-run health ministry said in a statement that the dead men were civilians, but the Popular Front for the Liberation of Palestine militant group said in a statement that they were its fighters. The national rescue service said at least seven people were wounded by the strikes.
The spokesman, Brigadier-General Ronen Manelis, told Army Radio that covert missions were mounted frequently, comments that suggested the Israeli force may have been gathering intelligence.
Israel's prime minister, Benjamin Netanyahu, cut short a visit to Paris, where he had been attending first world war commemorations.