The vile murder took place in Mogadishu, Somalia on Friday last week, and 11 arrests were made.
Police say they are still trying to identify other suspects.
Student Hamdi was due to enroll in college and her death sparked huge protests across the country.
In a statement, police said: “We have arrested 11 people in the recent rape case in the Wabari neighborhood of Mogadishu and efforts to track down and identify other suspects are ongoing. “
According to local media, Hamdi left his home at noon after arranging to meet a friend.
Her family then received a heartbreaking phone call informing them that her body was in a morgue.
MP Mustaf Sheikh Ali Duhulow told reporters: “The rape and murder of Hamdi has sent shock waves through Somalia, and nothing will be left behind to ensure that justice is done. ”
And his fellow MP Hassan Moalim added, “I want to tell the Somali people and my constituents that I will not rest until the late Hamdi gets the justice he deserves. ”
Horrified protesters say not enough is being done to tackle violence against women in Somalia.
Abdirahman Abdisahur, leader of the Wadajir party, tweeted: “We must collectively face this type of crime and reject it with one voice. ”
Bilan Bile, from the Somali National Women’s Organization (SNWO), told the Nation that a new campaign would be launched following the murder.
She said, “Our campaign will be designed as the universal ‘Me Too’ movement.
“We will encourage Somali women to let go of the negative attitude of seeing rape as something shameful. “