Sussex Police said the emergency services were called to the flat in Sutherland Avenue, Bexhill, at 13:35 BST.
The victim died from her injuries at the scene.
Following a police search, a 21-year-old man from Bexhill was arrested on suspicion of murder and is currently in custody. The suspect was known to the victim, police said.
A woman has died after being stabbed in a flat in East Sussex.