The men, all Iraqis, were arrested after the 16-year-old girl was assaulted on the outskirts of the Iraqi Kurdish region's capital Arbil on Tuesday, police said.
Three of the suspects had confessed to carrying out the assault, police added.
A police statement said the girl had been walking to her family's home in Arbil after finishing work at a local supermarket when three men snatched her and took her to a farm on the outskirts of the city.
Police said they proceeded to assault her sexually, and called three other men who also took part.
The six later abandoned the girl, who made her way back to the city and reported the incident, police said.
Three men were arrested late on Wednesday and three others more on Thursday, and the case has been referred to the courts, according to police.
Dozens of Syrian Kurdish protesters then gathered outside the autonomous Kurdish region's parliament on Thursday to call for the six suspects to be executed.
"We are calling for the maximum punishment, which is execution, for those men," said demonstrator Amama Hassan.
"At the same time, we are calling for freedom for women."
The protesters held placards including one reading "Do not violate my honor", and another that read "Do not be sad, sister... we will not be silent until the criminals are executed".
Syrian refugees in Iraq number more than 210,000, the vast majority of them in the three-province Kurdish region, according to the United Nations.
Though they have suffered sporadic incidences of violence in the region, most go unreported.
The assault is the most violent incident against a Syrian Kurdish refugee to be reported yet.
BA/BA