Met Police officers are also searching a property in Southwark, London, where they have found human remains.
Westminster officer Gordon Semple, 59, from Greenhithe, Kent, was last seen on 1 April in the London Bridge area.
Police said his family had been informed about the "significant development".
A spokesman said: "We are unable to make formal identification at this stage, but this is devastating news for all those involved in the search for Gordon."
Police who were called to an address on the Peabody Estate on Thursday afternoon found human remains, he said.
He said forensic work was under way at the scene which may take some time.
A post-mortem examination would be held in due course, he added.
He said police would not speculate about what had happened or any possible motive at this stage, and would not speculate on the cause of death until post-mortem tests had taken place.
On 1 April, PC Semple, who is originally from Inverness, had a work meeting at the Shard's Shangri-La hotel and left at about 12:30 BST.
He was seen on CCTV in Great Guildford Street at 15:00 BST and his partner reported him missing later that night.
PC Semple has no children but still has family in Scotland.
The man under arrest is being held in custody.
Detectives searching for a serving police officer who has been missing for six days have arrested a 49-year-old man on suspicion of murder.