The print size of a QR Code is an important matter that must not be ignored! QR Codes must be large enough to be recognized and decoded by the smartphone's reading application. Two topics have to be considered when designing your QR Code.
You ought not to print your QR Codes too small, or they could be unreadable (this is one of the most common mistakes). To be sure that your QR Codes are readable, do not print them in less than 3cm square (1.2 inches).
You can still choose smaller print sizes for your QR Codes, but you need to be careful.
QR Codes can be smaller (up to 1.5 cm square) and still be readable, but then they need not to contain too much data and to have less distorting customisations (placing a logo would not be wise for a small QR Code). Modern smartphones should be able to read them.
But don't forget the golden rule: always test the readability of your QR Codes by scanning them yourself!
The ideal print size of a QR Code is related to the scanning distance. First of all you must know when and how it will be scanned: on a large poster or on a product packaging? Scanning distances will be very different and QR Code print sizes will vary accordingly.