The fire and smoke caused an estimated $85,000 in damage, McGhee said.
The two-story house lacked a smoke detector, he said.
The house is owned by Paul E. Kramer of Appletree Lane in Williamsport and had only recently been rented, authorities said. The home is insured, the fire marshal said.
The house is one of the older homes in the historic town, authorities said.
It was built in the mid-1790s, and original rough-cut timber was visible from the basement level of the home, one firefighter said.
About 30 volunteer firefighters from Williamsport, Halfway and Fairplay responded to the blaze, which was brought under control 20 minutes after rescuers arrived, officials said.
There were some tense moments when the call for help came in, firefighters said.
Firefighters were initially given an incorrect address and went to East Potomac Street on the call, which stated that a child was hurt in a fire, firefighters said.
They quickly realized they were at the wrong house and learned the call was for the west side of Potomac Street, firefighters said. When firefighters arrived, the mother and toddler already were out of the house.
Traffic was detoured from the 100 block of West Potomac Street for several hours.