Three other women who, like Hojabri, built a following on Instagram with their dancevideos, have been taken into custody, according to the Asr-Iran news website.
"It wasn't incitement, I didn't want to encourage anyone, I didn't have an objective", she said.
The teenage gymnast reassured authorities that it was not her intention to do so.
"You will be laughed at if you tell people anywhere in the world that 17 and 18-year-old girls are arrested for their dance, happiness and beauty on charges of spreading indecency, while child rapists and others are free", wrote Iranian blogger and political dissident Hossein Ronaghi-Maleki. "I only do gymnastics".
On Saturday, the Iranian government channel First TV published the confessions of Instagram models, who admitted to "promoting moral deviation".
There has been widespread outcry over the arrest of Hojabri and the other detainees among Iranians in Iran and overseas, by artists, journalists, activists, politicians and thousands of ordinary citizens on social media. "We praise and admire her as a leader to let our voices for freedom to be heard".
Iranian authorities have previously cracked down on dancing. And when it comes to dancing, the rule is equally strict for both genders. Similarly, in August past year, six people were arrested for taking Zumba classes at a public square in Tehran. Their sentence - one year in prison and 91 lashes - was later suspended.