The raider gained entry by smashing a window at the home in Clayfield View, Mexborough, before stealing presents including jewellery, electronic items and money from cards.
He then fled the scene and headed towards Coniston Road flats.
Police have now released two CCTV images of a man they are tracing in connection with the incident, which happened on Sunday, December 20, at about 2.45pm.
PC James Harding said: “The occupants of this house have had their Christmas ruined by the offender responsible for this intrusive crime.
“The offender has opened all of the family’s Christmas presents and cards from their loved ones and has removed gift money from various cards.
“Along with a quantity of cash, a number of electronics and jewellery items were also stolen.
“The despicable actions of this offender have left the family extremely upset at what should be a very happy time of the year for them.
“We are keen to speak to the man pictured in this image and would ask anyone with information, or who knows who the man could be, to contact police.”
Anyone with information is asked to contact police on 101 quoting incident number 692 of 20 December 2015.
Crimestoppers can be also be contacted anonymously on 0800 555111.