US President Donald Trump has called on the Iranian government to remove the death sentences.
"To the leaders of Iran, I would greatly appreciate if you would spare this young man's life and not execute him. Thank you," Trump tweeted.
His cause is also being championed by the UFC community. Conor McGregor's coach John Kavanagh replied to Trump's tweet by saying: "Save Navid Afkari."
Ben Askren, a former UFC star and Olympic wrestler, added: "This is what a real authoritarian regime look like."
Afkari, who also works as a plasterer, has won several wrestling medals in Iranian tournaments. Wrestling is a beloved sport in Iran, and Iranian athletes have distinguished themselves in international freestyle and Greco-Roman competitions.
The news website Iran International reported Iran imposed two death sentences on Afkari as well as six years and six months in prison and 74 lashes.
One death sentence was imposed by a criminal court and one by a "revolutionary court".
Afkari's brother Vahid received a sentence of 54 years and six months in prison and 74 lashes. A third brother, Habib, was given a prison term of 27 years and three months and 74 lashes.
In a video reviewed by Fox News, the brothers' mother denounced the sham trial against her sons.
"I'm desperately asking for help from anyone who can hear my voice," she said.