In its quarterly figures yesterday the retailer picked out the product as the one that is driving sales outside its more traditional groceries.
The company said the gaming system, which responds to body movements to allow the player to play virtual games, is a big Christmas hit.
Along with the iPad, the hi-tech system, with a price tag of around £129, is driving sales faster than the shelves can be filled.
A Tesco spokesman said: “These are flying of the shelves and have really caught the imagination. We are not issuing precise figures, and there are no comparatives because it is new, but it is the must-have gift this Christmas. We have had to re-stock but they are available at the moment.”
Microsoft says at least 2.5m Kinect sensors have been sold and it is aiming for around 5m into January.