Officers were called to the flat in London Road, Bexhill, in the early hours of this morning (July 21).
A Sussex Police spokesman said: "Police have arrested a man on suspicion of murder after an incident at a Bexhill flat.
"At 12.35am on Sunday (July 21), officers were called to a disturbance at a flat in London Road, Bexhill.
"A 29-year-old woman was sadly found dead at the address and a 36-year-old man was arrested there on suspicion of murder. He is currently in custody for interview and further enquiries.
"Both people were known to each other and police are not looking for anyone else in connection with this investigation.
"Officers from the Surrey and Sussex Major Crime Team are investigating and no further information is available at this stage."