Firefighters were called to the home in Headrig in the Parkside end of the town at 2.35am today.
A fire service spokesman said a woman and girl were taken to Borders General Hospital for precautionary checks for the effects of smoke inhalation.
Three fire engines went to the scene and extinguished the blaze and crews remain at the house this afternoon.
A Police Sotland spokesman said: “Police received report of a fire at an address on Headrig in Jedburgh around 2.50am on Friday, November 22. An adult and a child were taken to Borders General Hospital as a precaution. There were no injuries.
“This was an electrical fire, non-suspicious and there is no further police involvement.”