"The terrorist was handed over to the supervision of a soldier, who, under suspicion, allegedly shot him, resulting in his death," the army said of the Sunday incident.
"In light of the preliminary information, a military police investigation has been initiated to examine the circumstances of the shooting," it added in a statement sent to AFP.
Hundreds of Palestinians have been detained since war broke out in October between Israel and Hamas.
Last month, the militant group called for an international investigation into "summary executions" of dozens of Gazans. The army said at the time that it was "unaware of" any such killings.
The push for a probe followed the announcement by the United Nations human rights office that it had received "disturbing" reports that Israeli troops had "summarily killed" at least 11 unarmed Palestinians in a possible war crime in Gaza.
Israeli troops also mistakenly shot dead three Israeli hostages in Gaza, while at least 18 soldiers have been killed in friendly fire incidents, according to military figures.
Several Palestinians have also died in custody over the past few weeks, a number of them in southern Israel, Israeli media reported.
The Israeli army has said that it is investigating the deaths of detainees captured during military operations in Gaza.
The army came under severe condemnation from human rights groups early last month after Israeli television showed scores of Palestinian men in military custody stripped naked on a Gaza street.
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