The issue arose on Friday and work is ongoing to try to resolve it.
A short statement from Dumfries and Galloway Council confirmed the problem had occurred at the end of last week.
It said it was working with the software supplier to identify the problem and repair it as soon as possible.
No date has yet been set for the return to operation of the library management system or the public access computers.
There is no access to e-books and limited access to online resources but books can still be returned or loaned.
There are more than 20 libraries situated throughout the region.
An apology has been issued for any inconvenience caused by the "unforeseen" computer shutdown.
An IT problem has shut down public access computers and a stock management system at libraries across Dumfries and Galloway.