Anyone with information is asked to call police on 101 or Crimestoppers, anonymously, on 0800 555 111.
Police officers, calling for a safe and well check, made the discovery of her body.
Concerns were raised after the 81-year-old woman had not been seen for some time.
West Midlands Police say the 41-year-old was detained on Saturday at a house in Ebrook Road around 3.30pm.
A West Midlands Police spokesman said: #8220;A post mortem examination is due to take place today.
They included the death of Ryan Passey, who died after allegedly being stabbed at Chicago nightspot in Stourbridge.