
Sirens sounded across cities and towns in the region – including Be’er Sheva, which is home to some 200,000 people.
The rockets were launched from locations around Gaza almost simultaneously, testing the capabilities of Israel's Iron Dome missile defence shield.
As many as 60 of the incoming rockets had been intercepted, the IDF said.
In response, the Israeli air force launched strikes on at least 70 locations within Gaza, targeting "compounds, observation posts and rocket-launching squads", as well as tunnels beneath the land border with Israel, the IDF said.
Three Palestinian men were killed in the strikes, the Gaza Health Ministry and Palestinian media said.
There was no immediate information on the unnamed passenger travelling on the bus hit by a rocket near the kibbutz of Kfar Aza.
He was taken to the Soroka University Medical Centre in Beersheba.
Photographs from the scene showed firefighters tackling a raging blaze on the vehicle, which was reduced to a charred shell.
Prime Minister Benjamin Netanyahu, who had returned to Israel early from Armistice Day commemorations in Paris to respond to violence in Gaza earlier in the day, was meeting senior IDF generals on Monday evening.