The protesters are described as students and they are said to have shouted "Those who insult the Koran must be condemned".
"Death to America" and "Death to Israel", common slogans in Iran, are also said to have been shouted.
The al-Azhar university in Egypt's capital Cairo, often described as the Sunni Muslim world's foremost institution, condemns the licensed burning of the Koran and calls for international legislation to "prevent abuse of the sanctity of the religion", reports Ekot on Swedish Radio.
Condemns burning
Several countries - such as Bahrain, Iraq, Jordan, Kuwait and Oman - have condemned the burning.
On Sunday, an embassy council at the Swedish embassy in Baghdad was summoned to the Iraqi Foreign Ministry.
According to the news agency AP, the ministry then warned that the burning of the Koran could have serious consequences for Sweden's relationship with the Muslim world.
The Swedish Ministry of Foreign Affairs (MFA) has previously confirmed to TT that the council was convened, but does not want to comment on what was said during the meeting.
TT has contacted the Ministry of Foreign Affairs for a comment on Monday's protests in Iran.