Footage of Aswad's death was later posted on the internet, where the videos showed what appeared to be uniformed members of a security force among the crowd.
Authorities have said Aswad was attacked and killed because members of her community believed she had run off to marry a Sunni Muslim man.
Aswad was a member of the Yazidi sect, a religious group, incorporating a number of ancient beliefs that does not allow marriage outside the faith.
"They [the crowd] brutally killed a young Yazidi girl in pursuit of out-of-date tribal rites," the AFP news agency quoted Tahsin Saeed Ali, the Yazidi religious leader known as the emir of the Yazidis in Iraq as saying.
The Kurdish Regional Government later condemned the killing and called for Aswad's killers to be brought to justice.
CNN and the Malaysia Sun reported the arrests, with CNN quoting local officials as saying they were looking for four more suspects, including one of Aswad's cousins.
Amnesty International, the human rights group, said it welcomed the Kurdish government's condmenation of the killing.
A spokesmen said Amnesty had requested "concrete measures to protect all those at risk of becoming victims of 'honour crimes".