The card explained that the burglar thought the property in Halifax, about 200 miles north of London, was empty and apologized for breaking in.
Police said the woman was "very shaken" by the confrontation.
"Whoever did this has a conscience, and feels guilty for what he has done," West Yorkshire Police Det. Insp. Tony Nicholson said in a statement.
Police said the burglar fled the house empty-handed and appealed for him to come forward.