"My daughter Kimia, you have triggered the happiness of all the Iranians, and particularly of the women. I wish you eternal joy," the president tweeted.
The message is accompanied by a picture showing Alizadeh, 18, draped in the Iranian flag as she celebreated Thursday her victory in Rio where she clinched the medal, beating Nikita Glasnostic of Sweden 5-1 in the taekwondo under-57kg division.
Even conservatives voiced their satisfaction over the teenager's win.
Fars news agency, which is close to the deeply conservative camp in Iran , hailed "Kimia who made history" and said in a report that the bronze medal she won "is worth gold".
In keeping with Iran 's strict Muslim custom, the teenager competed wearing a head scarf over her taekwondo outfit.
Alizadeh's victory was also celebrated on social networks by many of her compatriots, including popular actress Taraneh Alidoosti who sparked debate in Iran this year after she was pictured with a "woman power" symbol tattooed on her arm.
"The future will tell what you have achieved for your peers," tweeted
"You have bolstered their faith and showed them that (sports) belongs to them as well," she wrote.
Iranian women are banned from entering stadiums for major sporting events, including football, as part of a male-female segregation ushered in by Iran 's 1979 Islamic revolution.
In 1992, Lida Fariman was the first Iranian woman to compete at the Olympics in Barcelona in shooting.
This year, the Iran team at the Olympics comprised nine women out of a total of 41 athletes.
Alizadeh meanwhile told Iranian television she was very excited about her victory in Rio and hopes Iranian women will be able to clinch gold at the next Olympics.