Hamdi Mohamed Farah was lured to meet a male friend on Friday last week, September 11, but was attacked by a group of men in Mogadishu, Somalia.
11 arrests have been made so far and police say they are still trying to identify other suspects.
Student Hamdi had been set to enrol in college and her death has sparked huge protests around the country.
In a statement, police said: “We have arrested 11 people over the recent rape case in Wabari neighbourhood in Mogadishu and efforts to track and identify other suspects are ongoing.”
According to local media, Hamdi left her home at midday after arranging to meet a friend.
Her family later received a heartbreaking phone call informing them that her body was in a morgue.
MP Mustaf Sheikh Ali Duhulow told reporters: “The rape and killing of Hamdi sent shockwaves across Somalia, and no stone will be left unturned to ensure justice is served.”
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 she deserves.”
Demonstrators say not enough is being done to tackle violence against women in Somalia.
Abdirahman Abdisahur, leader of the Wadajir Party, tweeted: “We have to collectively confront this kind of crime and reject it with one voice.”
Bilan Bile, of the Somali National Women’s Organisation (SNWO) told the Nation that a new campaign will be launched in the aftermath of the killing.
She said: “Our campaign will be designed like the universal “Me Too movement.
“We will encourage Somali women to shed the negative attitude of seeing rape as an unmentionable occurrence.”