Mirzakhani studied math at Harvard, earning a PhD in 2004. She currently works at Stanford University as a math professor.
"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani said in a statement released by Stanford.
The International Mathematical Union, the organization that gives the award, said Mirzakhani won the prize for her "outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces."
The IMU awards the Fields Medal every four years. The winners are always announced at the opening ceremonies of the International Congress of Mathematicians annual conference, held this week in Seoul, South Korea.
Mirzakhani has stated that she was mostly interested in writing and literature as a young student, but that her brother's talk of his science learning piqued her interest in math.
"I can see that without being excited, mathematics can look pointless and cold," she said in a 2008 interview. "The beauty of mathematics only shows itself to more patient followers."
Mirzakhani was given the award for her contributions in the fields of geometry and dynamical systems. While her work is considered "pure math," her original and sophisticated impacts in these fields reportedly have implications in other areas of studies, including quantum physics, prime numbers theory and cryptography.
"Fluent in a remarkably diverse range of mathematical techniques and disparate mathematical cultures, she embodies a rare combination of superb technical ability, bold ambition, far-reaching vision, and deep curiosity," the ICM said in a statement.
Three others were also awarded the Fields Medal, including Artur Avila, Manjul Bhargava and Martin Hairer.