Abu Ubaida blamed the incident on what he described as Israeli "massacres" against Palestinians.
"The enemy government [Israel] bears full responsibility for these massacres and the resulting reactions that affect the lives of Zionist prisoners," Abu Ubaida said in a statement posted on Telegram.
He said a committee has been formed to investigate the details, and the findings will be announced later, adding that efforts are underway to save the two wounded hostages.
It is the first time that Al-Qassam has said its guards killed hostages. The group has often attributed previous killings of hostages to Israeli bombardment in the strip.
Israeli Army spokesperson Avichay Adraee said in Arabic on X: "In the last few minutes, the terrorist Hamas published a written report claiming that in two separate incidents, Hamas activists killed an Israeli captive and wounded two women captives. At this stage there is no intelligence document to confirm or refute Hamas' allegations. We continue to investigate the credibility of the statement and will provide information where we have it."
The development comes shortly after the Palestinian group named Gaza leader Yahya Sinwar, one of the masterminds behind the Oct. 7 attack on Israel, as its new leader following the assassination of former leader Ismail Haniyeh in Tehran on July 31.
On Saturday, an Israeli airstrike on a Gaza City school compound housing displaced Palestinian families killed around 100 people.
Israel on Monday said 31 militants were among the dead. Hamas and the Islamic Jihad denied the Israeli allegations, and said that no gunmen were present at the school.
The incident comes amid conflicting reports about expectations regarding the outcomes of talks aiming to end the war in Gaza slated for Thursday. Hamas on Sunday cast doubt on its participation in the anticipated talks.
(Reporting by Jaidaa Taha, Nidal Al-Mughrabi and Muhammad Al Gebaly; Editing by Leslie Adler)

Smoke rises above residential buildings after an Israeli air strike amid combat between the Israeli army and militants of the Al-Qassam Brigades, the military wing of the Hamas movement, at the beach road in western Gaza City, 08 November 2023. More than 10,000 Palestinians and at least 1,400 Israelis have been killed, according to the Israel Defense Forces (IDF) and the Palestinian health authority, since Hamas militants launched an attack against Israel from the Gaza Strip on 07 October, and the Israeli operations in Gaza and the West Bank which followed it. EPA-EFE/MOHAMMED SABER