Witnesses said explosions came from the vehicle after it was attacked, but there was no immediate independent confirmation that it had been carrying explosives.
Some residents said the truck appeared to have been disguised as an Israeli tank transporter.
Islamic Jihad has been behind several rocket attacks from the Gaza Strip into southern Israel. Shortly after the air strikes, several rockets hit Sderot, an Israeli town near Gaza, causing no casualties.
The Gaza Strip has been under the control of Hamas since June, when they defeated fighters from the Fatah movement of Mahmoud Abbas, Palestinian president.