Ch Insp Imran Mirza, from Sandwell Police, said: “Our thoughts remain with the woman’s family at this awful time who are being supported by specialist officers.
“This is a fast-moving investigation, and we have one person in custody for questioning.
“We are reviewing CCTV footage, carrying out house to house enquiries and examining forensic evidence.”
The force said there will be a larger police presence in the area to offer reassurance to the local community.