The ministry submitted a letter to the ICC of various crimes committed by Israel, particularly the "crime of execution" of Abu Akleh.
"As is the case with previous periodic reports, the ministry called on the ICC to adopt this report in order to expedite its investigations and bring criminals and murderers to international justice," said the ministry in a statement carried by Palestinian Authority's official news agency Wafa.
Fifty-one-year-old veteran Al Jazeera reporter Shireen Abu Akleh was shot dead by Israeli troops as she covered a security raid in the occupied West Bank's Jenin refugee camp on 11 May.
The death of the much loved media icon - who became a household name during the second Palestinian intifada and helped establish Al Jazeera as a major international network - was received with shock and outrage across the world.
Her killers have still not been brought to justice.
Palestinian officials and witnesses, including journalists who were with her, say she was killed by Israeli army fire. The military, after initially accusing Palestinians of being responsible, later backtracked and now say that it's "very likely" that Abu Akleh was killed by Israeli gunfire.
The Palestinian Journalists' Union says at least 55 journalists have been killed since the year 2000, which is when the Second Intifada took place.
In a recent report, press freedom watchdog Reporters Without Borders (RSF) said that Palestinian journalists are "systematically subjected to violence as a result of their coverage of events in the West Bank. Israeli reporters are barred from visiting the Gaza Strip."
Palestinian reporters are regularly subjected to arrest, violence and prosecution, with their equipment often destroyed and their accreditation cards withheld .