We recommend no smaller than 2cm (0.8") however the minimum size of the QR code will be dependent on:
The distance between the QR code and the scanning device, and hence the size the code will appear to be in the viewport of the scanning device - if you have one on the side of a building it would need to be very large because it's going to be scanned from a long distance, however if it's printed in a magazine then the scanning device will be held quite close to it.
The size of the dots in the code - As the data you put into a QR code increases, the number of dots that the QR codes needs to use to store that data increases accordingly. For a QR code of a given size this will result in progressively smaller dots being used and eventually they will reach a size that's below the resolution limit of the scanning device. As a general rule of thumb we recommend that your QR code should have no more than 50 rows and columns of dots to stay within the usual maximum resolution limits of most smartphone cameras.
Regardless of the size of the QR code, the finished QR code should be tested thoroughly in its intended final setting to make sure that it works at that size.