Police officers visited a house in Hayes at 9.38am on Monday after reports of concerns for a missing woman.
Inside the home, they found the body of a woman in her 30s.
They arrested a 26-year-old man who is believed to have known the victim.
He was in hospital being treated for injuries which are not life-threatening.
A murder investigation has been launched, and the Metropolitan Police say they are not looking for anyone else in connection with the woman’s death.
Her next of kin have been informed, but formal identification is yet to take place.
:: Anyone with information that may assist the investigation is asked to call the incident room on 020 8721 4205. To remain anonymous, call Crimestoppers on 0800 555 111.