Police were called to a home at Bromsgrove Cottages, Faringdon, at around 1.20pm on Tuesday and found the child dead.
Police have given no information about the age or gender of the child but said next of kin had been informed.
A murder investigation is now under way.
The senior investigating officer, Detective Inspector Dave Hubbard of the Thames Valley Major Crime Unit, said: “Following the discovery of a deceased child, we have launched a murder investigation.
“The next of kin have been informed and we are offering support to them.
“We are in the very early stages of this investigation and an arrest has been made in connection with this incident.
“We would ask anyone with information to please call 101 quoting reference 730 (14/03).
“If you do not want to speak directly to the police you can contact the independent charity Crimestoppers anonymously on 0800 555 111. No personal details are taken, information is not traced or recorded and you will not go to court.”
Local Police Area Commander for South and Vale of White Horse, Superintendent Rory Freeman, added: “This is a very shocking discovery and I am aware it may have a very direct impact on the community of Faringdon.
“In light of this incident there will be an increased police presence in the area to provide reassurance and we would advise any members of the community affected by this incident to speak to one of the Neighbourhood Policing Team.”