Fatou Bensouda's move comes after she launched a preliminary examination in September into Myanmar's 2017 military crackdown, which saw around 700,000 people flee into neighboring Bangladesh.
Bensouda will now "submit a request for an authorization to open an investigation into this situation," the Hague-based ICC said in a statement.
Judges will then "decide whether or not to authorize" her request for a full-scale probe, the court said, without saying when that decision would be made.
In September, judges ruled that even though Myanmar has not signed up to the ICC, the court still has jurisdiction over crimes against the Rohingya because Bangladesh, where they are now refugees, is a member.
The probe would be "within the context of two waves of violence in Rakhine State on the territory of the Republic of the Union of Myanmar," and other crimes that were "sufficiently linked" Bensouda said in a letter to the court.
Officials from the ICC have since visited Bangladesh as part of the prosecutor's preliminary enquiries.
UN investigators have separately called for the prosecution of top Myanmar generals for "genocide."
Myanmar's army has denied nearly all wrongdoing, insisting its campaign was justified to root out Rohingya insurgents who staged deadly raids on border posts in August 2017.
It has also "resolutely" rejected the ICC's assertion that it has jurisdiction over the crime, saying that the decision was in "manifest bad faith" and was of "dubious legal merit. – Rappler.com