The woman was found dead by paramedics at 07:25 BST on Sunday morning
A 42-year-old man has been arrested on suspicion of killing his ex-partner and trying to kill their two children
The 42-year-old woman was found dead at an address in Woodlands Farm Road, Pype Hayes, north Birmingham, police said.
A 15-year-old boy suffered a punctured lung while a nine-year-old girl suffered "strangulation-type" injuries, West Midlands Police said.
Police arrested the man, from Sutton Coldfield, on suspicion of murder and attempted murder.
Paramedics from West Midlands Ambulance Service pronounced the woman dead at 07:25 BST on Sunday.
Her death is being treated as unexplained and a post-mortem examination will take place on Tuesday, police said.
Police said they believe both children, who are recovering in hospital, were attacked in their sleep.
Det Insp Paul Joyce said the force was not looking for anyone else in connection with its investigation.