Emergency services were called at 1.35pm to a flat in Sutherland Avenue after receiving a report of a stabbing. A 20-year-old woman sadly died at the scene.
Police carried out a search of the area for the suspect, who is known to the victim, and arrested a 21-year-old Bexhill man on suspicion of murder. He is currently in custody.
DCI Mike Ashcroft, of the Surrey and Sussex Major Crime Team, said:
We are in the early stages of the investigation and are appealing to anyone who heard any disturbance or saw anything suspicious around this time in Sutherland Avenue to contact police.
Anyone with information should contact police on 101 or email email@example.com quoting Operation Rockingham or ring the independent charity Crimestoppers anonymously on 0800 555111.