Mirzakhani, 40, fought with cancer for four years and was hospitalized lately as the cancer has spread to her bone marrow.
She made history in 2014 after becoming the first woman, as well as the first Iranian, to win the Fields Medal - nicknamed the "Nobel Prize of mathematics" - for her outstanding contributions to the fields of geometry and dynamical systems.
Iranian officials received heavy criticism for not using more recent pictures of Mirzakhani with short, uncovered hair, as she appeared at Fields Medal awarding ceremony.
"A light was turned off today. far too soon".More news: KJo walks IIFA ROCKS green carpet in red
Firouz Naderi, her friend and NASA scientist, confirmed Mirzakhani's death on Instagram. When her Fields Medal award was announced there, the photo used showed her not wearing an hijab.
"It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out", she added.
Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita - who once referred to her mother's work as "painting", because of the doodles and drawings that marked her process of working on proofs and problems, according to an obituary released by Stanford.
Iranian Foreign Minister Mohammad Javad Zarif paid tribute to her.More news: Twitter goes berserk as Mithali Raj scores sixth ODI century
In a tweet, Gary Lewis, UN Resident Coordinator for the Islamic Republic of Iran, also expressed his sorrow over Mirzakhani's death.
A year later, she became the first Iranian student to achieve a flawless score and win two gold medals at the Olympiad. The 40-year-old, who used to teach at Stanford University, was also the first Iranian woman to be elected to the US National Academy of Sciences (NAS) in May 2016 in recognition of her "distinguished and continuing achievement in original research".
Mirzakhani studied mathematics in Iran and earned a PhD degree from Harvard in 2004.More news: Greystones man dons skirt to join women's doubles match at Wimbledon
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