The device, which has hit UK shelves today and is priced at £129.99, is an add-on that will enable Xbox users to play games by moving parts of their body, rather than a handheld controller. The technology can also identify different people's faces and recognise different voices.
According to electronics retailer Best Buy, the device is likely to be to be one of the most popular products in the run up to Christmas.
"We are preparing ourselves for brisk demand for the Kinect, especially with Christmas present buying now on most people's minds. Availability is very limited and on a first-come, first-served basis, but we expect deliveries between now and Christmas," said Harry Parmar, commercial director at Best Buy UK.
"Following the success of the Nintendo Wii, and the Sony Playstation 3 and its Move device, increasingly consumers are looking to gaming devices as a way to have fun with friends and family and to keep active."
Microsoft Kinect also ships with a copy of Kinect Adventures - a game collection compatible with the motion-sensing camera that includes a white water rapids race and a ball batting game.