The professor at Stanford University in California was among four Fields Medal recipients at the International Congress of Mathematicians held in Seoul, and the first female among the 56 winners since the prize was established in 1936.
"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani was quoted as saying on Stanford's website. "I am sure there will be many more women winning this kind of award in coming years," she said.
Mirzakhani, 37, was born in Tehran and lived there until she began her doctorate work at Harvard University. She said she had dreamed of becoming a writer when she was young, but she pursued her enthusiasm for solving mathematical problems.
"It is fun – it's like solving a puzzle or connecting the dots in a detective case. I felt that this was something I could do, and I wanted to pursue this path," she said.
Mirzakhani was recognised for her work in understanding the symmetry of curved surfaces, according to the Stanford site.
The prizes are awarded every four years. Wednesday's prizes were presented by South Korean President Park Geun-hye, the first woman to hold that post.
The other three Fields Medal winners on Wednesday were Artur Avila of the National Center for Scientific Research in France and Brazil's National Institute for Pure and Applied Mathematics; Manjul Bhargava of Princeton University and Martin Hairer of the University of Warwick in the United Kingdom.