The 40-year-old Iranian, a professor at Stanford University, had breast cancer which had spread to her bones.
Nicknamed the "Nobel Prize for Mathematics", the Fields Medal is only awarded every four years to between two and four mathematicians under 40.
It was given to Prof Mirzakhani in 2014 for her work on complex geometry and dynamical systems.
Iranian President Hassan Rouhani said Prof Mirzakhani's death caused "great sorrow," state media reported.
Foreign Minister Mohammad Javad Zarif said her death was a cause for grief for all Iranians.
