The man from Plymouth, Tobago, reportedly entered the apartment through a window, proceeded to lock all the doors, turn off the lights and set the building on fire before escaping.
Inside the house, were 50 year old Sherma McPherson and her 23 year old daughter Jamelia Roberts, who were forced to escape the blaze by jumping from the first floor of the apartment building.
Earlier in the day the suspect reportedly had an argument with McPherson.
Police said within a matter of minutes, officers from the Wrightson Road Fire Station arrived on the scene and put out the blaze. No other apartment in the building was damaged.
The suspect is expected to be charged and taken before a Port of Spain magistrate this week.