Maryam Mirzakhani, a Harvard educated mathematician and professor at Stanford University in California, was one of four winners announced at the group's conference in Seoul.
An expert in the geometry of unusual forms, she has come up with novel ways to calculate the volumes of oddly-shaped hyperbolic surfaces, which can be curved like a saddle or curly like a piece of crochet.
"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.
Mirzakhani was born in Tehran in 1977 and earned her PhD in 2004 from Harvard University.
She has previously won the 2009 Blumenthal Award for the Advancement of Research in Pure Mathematics and the 2013 Satter Prize of the American Mathematical Society.
The Fields Medal is given out every four years, to four separate winners.
The other three winners this year were Artur Avila of France, Manjul Bhargava of Princeton University in New Jersey, and Martin Hairer of the University of Warwick in Britain.
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