The west African nation accused Myanmar at the International Court of Justice in 2019 of breaching the UN genocide convention over a bloody 2017 crackdown.
Hundreds of thousands of minority Rohingya fled the Buddhist-majority South-East Asian country during the operation, bringing with them harrowing reports of murder, rape and arson.
The Hague-based ICJ said in a statement that it will at 1300 GMT "deliver its judgment on the preliminary objections raised by Myanmar".
Myanmar says the court should dismiss the case on legal grounds while it is still in its preliminary stages, and before it starts dealing with the genocide allegations in full.
It says the ICJ has no jurisdiction because mainly-Muslim Gambia is bringing the case as a proxy of the Organisation of Islamic Cooperation.
Countries are only allowed to file cases at the ICJ, which has ruled on disputes between UN members since just after World War II, as individual states.
The Gambia says it is supported by the 57-member OIC, which groups Muslim nations around the world
Myanmar also argues that the case is inadmissible as the Gambia is not a direct party to the alleged genocide, while Myanmar itself has also opted out of a relevant part of the genocide convention.
Finally, it also says the case should be thrown out as there was no formal dispute at the time the Gambia filed it, which is one of the court's rules.
If the ICJ rules against Myanmar, the case can move ahead to full arguments on the merits of the allegations of mistreatment of Rohingya Muslims.
A final judgment in such a case could take years.
Around 850,000 Rohingya are languishing in camps in neighbouring Bangladesh while another 600,000 Rohingya remain in Myanmar's southwestern Rakhine state.
Myanmar was originally represented at the ICJ by Nobel laureate Aung San Suu Kyi, but she was ousted as civilian leader in a coup last year and is now in detention.