Argentina adheres to the principle of universal jurisdiction, which means cases can be taken on regardless of where the alleged crimes were committed.
If the Rohingya case succeeds, it will be the first time the leaders of the Asian country, including State Councillor Aung San Suu Kyi, are judged on allegations of genocide against the ethnic minority.
"With today's legal case, we are urging Argentina to help us in our struggle, and to investigate those guilty of atrocity crimes," the Burmese Rohingya Organisation UK (Brouk) said in a statement on Wednesday, Efe news reported.
The organisation said it was being represented in Argentina by the former United Nations Special Rapporteur on human rights in Myanmar, Tomás Ojea Quintana.
Tun Khin, the lawyer who filed the complaint in the federal courts of Buenos Aires along with the president of Brouk, told Efe the main goal was for the Rohingyas to have the jurisdiction that would lead to an investigation into the alleged perpetrators.
"The Rohingyas, knowing that in Argentina certain antecedents of universal justice exist have decided from the symbolic and practical point of view to present this denunciation," Ojea added.
The case presented on Wednesday warned of decades of violence and oppression imposed on the Rohingyas in Myanmar's western Rakhine state.
"In 2016 and 2017, the Myanmar security forces and their proxies launched vicious 'clearance operations' against the Rohingya, killing thousands, committing widespread sexual violence, burning whole villages to the ground and driving some 800,000 people to flee into Bangladesh," the Brouk statement said.
It is also warned that the Rohingyas were "trapped in a virtual open-air prison where they often cannot access basic services such as education and health, are effectively denied citizenship, and face severe restrictions on their freedom of movement".
Ojea said the complaint, which was being supported by Grandmothers of the Plaza de Mayo, a human rights organisation set up to find children who were stolen during Jorge Videla's dictatorship, and Foundation for Peace and Justice humanitarian organisations in Argentina, seeks to open a judicial process that the Rohingyas say they cannot have in Myanmar.
"There are no independent courts," he said.
The International Criminal Court opened a preliminary investigation last year into allegations of deportation of Rohingyas to neighbouring Bangladesh.
In July, the ICC said the prosecutor was seeking an investigation into alleged crimes against humanity and persecution of the Rohingya people since October 2016.
Myanmar is not a member of the ICC, which complicates matters from a legal standpoint.
On Monday, The Gambia took a lawsuit to the International Court of Justice accusing Myanmar of genocide against the Rohingyas.
( With inputs from IANS )