The woman, who has not been named, is being held after police were called to reports of a stabbing at about 23:00 BST last night.
Ambulance crews and police found the 44-year-old woman with stab wounds and took her to Royal Devon and Exeter Hospital. She is not believed to be in a life-threatening condition.
Before police arrived at the address in Mincinglake Road, ambulance crews had discovered the boy, who was later pronounced dead at hospital.
"A 23-year-old woman was arrested at the scene on suspicion of attempted murder," a police spokeswoman said. "She remains in custody at Heavitree Road police station."
"The child's death is being treated as suspicious and a full forensic post-mortem will take place later today."
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