The airstrike before dawn Monday targeted a police post, the Palestinian news agency Ma'an said.
Palestinian medical sources in Gaza identified the police officer as Mohammed Kilani and said four other officers were injured in the strike, two seriously.
On Sunday, a Qassam rocket fired from Gaza exploded in the Sha'ar Hanegev regional council district but there were no reports of damage or injuries, the army said.
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U.S., allies launch airstrikes against Syria