The lawsuit following an investigation by the television news network's legal team, Al Jazeera said on Twitter.
The ICC must identify the individuals who were directly involved Abu Akleh's killing, Al Jazeera lawyer Rodney Dixon KC told a news conference in The Hague on Tuesday.
"The rulings of the International Criminal Court stipulate that those responsible be investigated and held accountable. Otherwise, they bear the same responsibility as if they were the ones who opened fire," Dixon said.
The circumstances of Abu Akleh's killing are disputed.
Israeli Prime Minister Yair Lapid said on Tuesday that no one would question Israeli soldiers.
"No one will interrogate IDF soldiers and no one will preach to us about morals of combat, certainly not the Al Jazeera network," Lapid said.
(Reporting by Lina Najem, Riham Alkousaa and Ari Rabinovitch; Editing by Frank Jack Daniel and Barbara Lewis)
Palestinians walk in front of a mural for Al Jazeera journalist Shireen Abu Akleh in the West Bank city of Bethlehem, 16 May 2022. Al Jazeera journalist Shireen Abu Akleh was killed on 11 May 2022 during a raid by Israeli forces in the West Bank town of Jenin. EPA-EFE/ABED AL HASHLAMOUN