There was no immediate claim of responsibility from Gaza militants for the rocket firing or comment from Hamas, the Islamist armed group that rules the coastal Palestinian enclave.
Police said there were no casualties or damage caused by the early morning explosion.
After nightfall, Israel's military said it struck at "terrorist targets in the Gaza Strip."
Hamas Radio said some of the group's security posts and a training camp were targeted by Israeli aircraft and tanks. There were no immediate reports of casualties.
Hamas occasionally test-fires rockets, launching them toward the sea. But the launch was probably caused by a malfunction, Hamas-affiliated Paltimes news website said.
The Israel-Gaza frontier has been largely quiet since an 11-day war in May in which 253 Palestinians were killed according to Gaza medical officials. Palestinian rockets and missiles killed 13 people in Israel during the May fighting.
But on Wednesday (December 29), gunfire from Gaza that wounded an Israeli civilian drew tank fire from the Israeli military, wounding three Palestinians.