Police said that emergency services, including the air ambulance, were called to an address in Stonefield Way at about 10.15pm on Wednesday (January 26) after concerns for a woman were raised.
Despite the best efforts of paramedics who commenced CPR, the 55-year-old woman, from Burgess Hill, was sadly declared deceased, police said.
A Sussex Police spokesperson said: “A 79-year-old man from Burgess Hill, who is known to the woman, has been arrested on suspicion of murder and remains in police custody.”
Detective Chief Inspector Matthew Durkin said: “Our thoughts are with the friends and family of the woman at this incredibly difficult time.”
“A man known to her has been arrested on suspicion of murder and our priority is to establish the full circumstances of this tragedy,” he said.
Chief Inspector Durkin added: “We are treating it as an isolated incident with no threat to the wider community, and the public can expect to see a heightened police presence in the area as our enquiries continue.”
He urged anyone with any information about the incident to report it online or call 101, quoting Operation Yelverton.
People can also contact the independent charity Crimestoppers anonymously on 0800 555 111 or report it online.