The woman’s body was found at an address in Crossley Street, in Netherton, Dudley, at around 12.40pm on Thursday.
West Midlands Police say the woman’s death is currently being treated as unexplained.
She is yet to be formally identified by officers. A resident who lived nearby said she believed the woman who lived at the property was ‘in her 30’s’.
A 38-year-old man has been arrested on suspicion of murder and remained in custody last night for questioning.
A police presence remained at the scene on Thursday evening, with a cordon stretching between Crossley Street's junctions with Northfield Road and Halesowen Road. Forensics were pictured earlier in the day heading into the house.
A West Midlands Police spokesman said: “We are investigating after the body of a woman was found at an address in Crossley Street, Netherton, this afternoon . We were alerted to the discovery by ambulance service colleagues just before 12.40pm.
“The death of the woman is currently being treated as unexplained and a scene is in place for enquiries to continue.
“A 38-year-old man has been arrested on suspicion of murder and remains in custody for questioning.”
Neighbours in the area have spoken of their shock after the woman's death. Hayley Morton said: "It's shocking – the area has been a bit bad lately, but you have never heard of murder here. I saw the man get arrested. Forensics have been here all day. They were boyfriend and girlfriend I believe."
A local businesswoman, who did not wish to be named, said: "We thought it was quite a nice area around here."
Another added: "It is just so shocking to see."
Anyone with information is urged to call West Midlands Police on 101, quoting log number 1850 of November 12. Alternatively, call Crimestoppers anonymously on 0800 555111.