Activist Tess Asplund took part in a counter-demonstration during a Nordic Resistance Movement (NRM) rally in Borlange on Sunday.
She has been widely praised on social media, including by Harry Potter author J K Rowling, who has called her "magnificent".
Ms Asplund said she was "shocked" by the reaction.
The anti-racism activist told Swedish P4 radio station that her act was an impulse, as she thought the neo-Nazi demonstration should not be being held there.
Some 300 people attended the march. Others joined the counter-demonstration, many wearing clown costumes.
The picture, by photographer David Lagerlof, has been widely shared on social media and by newspapers and websites around the world.
Ms Asplund said it would be "great" if the photo made people pay more attention to the fight against racism and xenophobia but that she did not want to be seen as a symbol.
On Twitter, many users called her "hero" and "amazing". Others noted her "unbelievable bravery" and "courage".
A message of support from British author Ms Rowling has been retweeted more than 6,000 times and liked by more than 12,000 people.
Neo-Nazi movements have been on the rise in Sweden and other European countries as a result of the migration crisis. The anti-immigration Sweden Democrats Party is the third biggest political force in the country.
The country, which has a decades-old reputation for welcoming refugees and political asylum seekers, has introduced tighter border controls in an attempt to control the influx.
Alongside Germany, Sweden is one of the main destinations for migrants trying to reach Europe. Tensions there have been heightened by arson attacks on asylum centres and other cases of violence.
A photograph of a woman with her fist raised defying a uniformed march of neo-Nazis in Sweden has gone viral.