Dunya's father, former President of the Maldives Maumoon Abdul Gayoom, and brother Ahmed Faaris Maumoon
were arrested on charges of trying to topple the Yameen government.
Dunya has been under fire for working with the government while her father and brother are in police custody after a state of emergency was declared in the country.
She today resigned from the Cabinet, calling upon the international community to support the Maldivian people in overcoming the political crisis and to help build a stronger democratic system.
More From This Section
Her father, Gayoom, is Yameens half-brother and ruled the country for 30 years until 2008. He was arrested at his residence early this month.
He is not just my father, but the father of the nation, who has built this country and has earned the respect and love of the people, she said in the letter.
Male, which has seen several political crises since the ouster of its first democratically-elected president Mohamed Nasheed in 2012, plunged into chaos early this month when the Supreme Court ordered the release of nine imprisoned Opposition politicians, maintaining that their trials were "politically motivated and flawed".