Ms Karaglanova had recently started a new relationship and had planned a holiday to The Netherlands to celebrate her birthday on 30 July, according to Russian daily Moskovsky Komsomolets (MK).
But her parents grew concerned when attempts to contact her in the days leading up to her trip had failed.
They then contacted her landlord and requested access to her apartment, where they found a suitcase containing her body in the hallway.
Her father requested an ambulance, but Ms Karaglanov was reportedly already dead with a slit throat.
The Police said there was no evidence that any struggle had taken place at the apartment, and no weapon was found at the scene, MK reported (in Russian).
They added that CCTV footage had captured a former boyfriend of Ms Karaglanov briefly visiting her property in the days around her disappearance, but did not say if this was being investigated further.
Ms Karaglanov regularly posted images of herself on Instagram. Her followers likened her appearance to the film star Audrey Hepburn.