The rocket from Gaza was shot down, according to the Israeli military, which confirmed early Thursday morning local time that airstrikes had begun.
It is unclear if anyone was injured in the attacks.
The atmosphere in the area is now more tense than in a long time, after attacks from both sides claimed more than 40 lives in recent weeks.
US Secretary of State Antony Blinken visited Ramallah and Jerusalem this week with a call for calm.
Israel's new right-wing government contains extreme nationalists who advocate an ever-harder and larger occupation of the West Bank.
And the Palestinians are deeply divided, both in their attitude towards Israel and among themselves in the West Bank and the Gaza Strip.