- Police Scotland said "following extensive inquiries" the mother-of-three was believed to have died, but her body has not been found.
- Det Ch Insp Bob Williamson, of Police Scotland’s major investigation team, said Ms Smith’s family had been made aware of the arrest.
A 39-year-old man has been arrested over the death of Khasha Smith in Edinburgh.
Ms Smith, 35, was last seen alive on a FaceTime call in October last year but was not reported missing until 5 January.
Police Scotland said "following extensive inquiries" the mother-of-three was believed to have died, but her body has not been found.
Specialist police teams searched an area near Calder Grove on Wednesday, close to where she lived with her partner at the time of her disappearance.
Det Ch Insp Bob Williamson, of Police Scotland’s major investigation team, said Ms Smith’s family had been made aware of the arrest.
He said: "Our thoughts are very much with Khasha's family at this extremely difficult time and they continue to be supported by specialist officers.
“They are understandably devastated and it is vital we get answers for them.
"Extensive inquiries remain ongoing to trace Khasha and I would again encourage anyone with any information regarding her disappearance to contact police, as a matter of urgency.”
Ms Smith was last seen safe and well during the video call with a friend on 10 October last year.
Timeline of Khasha's disappearance
10 October 2023: Khasha is last seen "safe and well" at home in Calder Grove, Edinburgh.
4 November 2023: Khasha last thought to have contacted family members, but no longer believed to have been "safe and well".
5 January 2024: She is reported missing by family months after last contact.
7 January 2024: Police Scotland appeal for information launched.
12 January 2024: Police Scotland's major investigation team takes over probe into Khasha's disappearance.
21 - 24 January 2024: Officers carry out fingertip search of woodland, metal containers and Union Canal culvert near Khasha's flat.
4 March 2024: Khasha's daughter, Calley, and mother, Nicola Neil, appeal for information five months on from last sighting.
4 September 2024: Specialist police teams search area near Calder Grove.
6 September 2024: Police say Khasha is believed to be dead and arrest a 39-year-old man over her death.
Ms Smith's daughter, Calley Smith and mother, Nicola Neil issued a plea for information in March.
In January, officers had searched Ms Smith's home, as well as a small section of the Union Canal about a hundred yards away from the flat.
A nearby woodland and metal containers close to the estate were also been searched.
On Wednesday, during a new search near her home, police said they remained open-minded and were doing everything they could to find her.
But officers also said they had to consider the possibility that Khasha may have come to harm.