Staff at the children's ward at Southampton General Hospital noticed the locked cupboard had been broken into and a Playstation 3 was missing.
It is thought the culprit may have been disturbed as other items were left.
CCTV on the ward, where visitors have to be let in by staff, is being reviewed. Police are investigating.
The ward's senior matron said the gifts made a "huge difference" to patients.
Cath Battrick added: "We don't have a budget for these sort of things, we rely completely on donations.
"Nobody likes being in hospital, especially at this time of year, so just having some form of distraction and entertainment makes a difference to their day.
"I hope they've got a conscious and return the item.
"Since this happened, we've had one donation of another Playstation so it looks like the children will not go without."
A JustGiving page has also been set up and has already raised more than Â£1,000 for the children's ward.
A thief stole a games console from a hospital during a raid on a toy cupboard full of toys and gifts for sick children.