"On 5 October, after 11 months of providing mental health care on Nauru, the Nauruan government informed MSF that our services were "no longer required" and requested that our activities cease within 24 hours", the global humanitarian organisation said in a statement on Saturday.
Hundreds of asylum-seekers and refugees are detained in Nauru indefinitely at the behest of Australia - including about 120 children.
The organisation started providing free "one door for all" psychological and psychiatric services on the island in 2017.
"The relationship between Medecins Sans Frontieres and the Nauruan government is a matter for them", Health Minister Greg Hunt told ABC radio on Monday.
"For us, we have been working with International Health and Medical Services, we will continue to focus on them".
Its abrupt dismissal follows a report by two prominent Australian refugee organisations saying most refugee children on Nauru are experiencing life-threatening mental health problems, including not eating or drinking and suicidal symptoms.
Australia funds a quarter of Nauru's annual national budget, with more than $20 million of foreign aid each year.
He said a process was available for dealing with cases which could not be managed locally.
"At this stage MSF wishes to reiterate our strong commitment to providing quality mental health care to all those in need on the island", a spokesman said.
The medical charity Medecins Sans Frontieres, also known as Doctors Without Borders, says the Pacific Island of Nauru has ordered it to stop providing mental health care services to the residents, as well as the asylum seekers that Australia houses in detention centers there.
It indicated a desire to find a way to continue its work.
"The Australian government has and continues to provide appropriate healthcare and mental health support to refugees and asylum seekers through contracted service providers", the department said.
MSF uses more than 30,000 doctors, nurses and other mostly volunteer personnel to provide medical aid in more than 70 countries.
The federal government on Sunday announced an inquiry into Australia's mental health system.