The teacher died and two other members of staff were hurt when an Israeli surface-to-surface missile struck an agricultural school in the northern town of Beit Hanoun, Hamas security forces said.
It released no further details, and school officials were not immediately available for comment.
Residents said Israeli tanks and heavy bulldozers broke the border fence to gain access to the Gaza Strip.
Israeli forces regularly carry out raids in the Gaza Strip in what they say is an effort to stop Palestinian fighters from launching rockets into southern Israel.
David Chater, Al Jazeera's correspondent in Gaza, reported: "There is no answer, as far as the Israel security forces are concerned, to these rocket attack from the Gaza Strip.
"That's why many people fear that the Israeli ministry of defence is beginning to look at plans for a much larger incursion into the Gaza Strip."
On Wednesday, a Hamas rocket hit Kibbutz Beeri, an Israeli communal village about 6km from the border fence, police said.
Two sisters, aged 12 and two, were hurt as they played in their yard, but escaped serious injury.
Their mother was taken to a hospital and treated for shock.
After nightfall on Wednesday, Israeli aircraft raided a metal workshop in central Gaza, Hamas said. No one was hurt.
The Israeli military had no immediate comment.
Hamas claimed responsibility for a suicide bombing that killed a woman in the Israeli town of Dimona on Monday.