Police were called to the property in the Ancoats area of the city at 7.40am on Tuesday, following reports that a man had jumped from a second-storey flat window.
Officers then received reports that a number of people had been assaulted, after which they gained entry to the flat in Swan Street and found the body of a woman.
Blood was visible on a top-floor flat window, with a nearby car suffering damage to its door and windscreen.
Witnesses told the Manchester Evening News that a man had been on a rampage.
Road closures remain in force in and around the area, and the suspect is in custody for questioning.
Greater Manchester Police Superintendent Chris Hill said: “We are currently working to establish the exact circumstances surrounding what has happened this morning and the woman’s death.
“Her death is currently being treated as suspicious and we have a team of officers working at the scene.
“We are in the very early stages of our investigation, however I would urge anyone with any information to please get in touch.”
:: Anyone with information should call police on 101, quoting reference number 327 of 13/02/18, or Crimestoppers, anonymously, on 0800 555 111.