The teaser trailer appeared on BBC Worldwide's YouTube channel but was then promptly taken down.
Doctor Who TV noted the trailer before its removal, recording the video's description.
The site claims that "gamers can take on the role of The Doctor and River Song as they explore the universe of Doctor Who over multiple time periods".
The teaser trailer ends with logos indicating that it will release for PC as well as PlayStation 3 and PlayStation Vita as a downloadable title.
The game is being developed by Supermassive Games, which previously worked on Sackboy's Prehistoric Moves and Tumble for PlayStation 3 using the PlayStation Move controller.
The Doctor Who Christmas special, 'The Doctor, the Widow and the Wardrobe', will air on December 25 on BBC One.
> Doctor Who Christmas Special - new pictures
Watch the trailer for the Doctor Who Christmas special below: