The wilful fire-raising in Dalkeith happened on Sunday at about 02:50 at a house in Allan Terrace in Dalkeith.
Firefighters put out the blaze quickly and police officers have appealed for information.
Det Insp Mark Henderson, of Police Scotland, said:  "We are appealing for any witnesses who may have seen suspicious activity in the Allan Terrace area on Sunday night."
A suspicious fire in a Midlothian house is being investigated by police.