There was no immediate retaliatory rocket fire from Gaza, or reports of injuries from either side.
The Israeli military says it struck several militant sites in Gaza after a rocket fired from the Palestinian territory hit a building in southern Israel.
The army said Israeli warplanes attacked several targets in Gaza early on Friday, including military and naval compounds belonging to Hamas, the militant group that controls the territory.
There was no immediate retaliatory rocket fire from Gaza, or reports of injuries on either side.
The Israeli army said the rocket launched late on Thursday hit a religious school in the Israeli border of Sderot.
The flare-up, which came after Israel this week closed Gaza's offshore waters to fishermen in response to the launch of incendiary balloons, breaks a month-long lull.
A ceasefire between Israel and Hamas reached in May halted the worst bout of violence since a 2014 war.