Carew was the third son of Sir William Carew, a Devonshire gentleman, and was born at Ottery Mohun (now Mohuns Ottery) in the parish of Luppitt. He attended grammar school in Exeter, where he was a frequent truant, and at St Paul's School. By his own account (set down in his biography) he once climbed a turret on Exeter city wall and threatened to jump if his master came after him. His father then had him led back to his house on a leash, like a dog, and for punishment coupled him to one of his hounds for a time.