Third-year students Felicity Chapman and Beth Kervin received the awards at a ceremony in Sydney.
AMA President Mukesh Haikerwal said the scholarships, worth $9,000 each, are aimed at attracting indigenous students towards the medical field.
He said it's important for young Australians, particularly those from an Aboriginal or Torres Strait Islander background, to aim high.
"Australia needs more indigenous doctors," said Dr Haikerwal.
"Around 2.4 percent of the Australian population is indigenous and the medical workforce should reflect this number. I hope the AMA's scholarships help in some small way to attract indigenous kids to medicine," he said.
Felicity Chapman, who hails from Grafton, said she enjoys studying medicine and hopes to be able to give back to her community.
She said her grandmother and aunt, both registered nurses, and their work with remote communities in NT have provided great inspiration.
"I am excited about the prospect of working in our Aboriginal Medical Services, working with elders to integrate our mob's understanding of health and healing into the way in which I approach medicine," she said.
Beth Kervin said she was inspired to follow a medical path by the Indigenous Entry Program while in her final year of high school.
She said she is looking forward to working in NT and "on the land that my people came from in Guyra", as well as her local area in suburban Sydney.
"If a population is to be successful and prosperous, the first thing they need is their health," said Ms Kervin.
"It is so important to encourage indigenous people, who have an enormous potential to make a difference to their own lives and the lives of the people around them, through both active encouragement and by simply being an example," Ms Kervin said.
The AMA scholarships were set up in 1999.