Police have issued an appeal for witnesses after the woman was found dead inside a tent at a caravan and camping site off Marine Parade at around 7am.
A 28-year-old man from Littlehampton has been arrested on suspicion of murder, police have confirmed.
No one else is currently being sought in connection with the death, police said.
Detective Inspector Andy Eggleton said: “We would like to speak to anyone who used a footpath giving access to the campsite between midnight and 6.30am on Sunday and who may have seen or heard anything suspicious.
“We are also aware of a 50th birthday party having taken place at the campsite this weekend, and again would ask anyone who attended to come forward, please.”
Anyone with information is asked to contact Sussex Police online or by phoning 101, quoting Operation Cobblestone.
Alternatively please visit the Crimestoppers website or call the independent charity anonymously on 0800 555 111.