Cradley Library, which will also be redecorated at the same time, will be shut from November 4.
The council says the cost of the refurbishment work is expected to be around £17,000.
It is the latest library in the borough to be given a revamp and follows work at Dudley and Netherton libraries.
Councillor Stuart Turner, cabinet member responsible for libraries, said: "Unfortunately we need to close the library in order for these essential improvement works to be carried out, but would remind library users that other libraries are available nearby including Halesowen, Long Lane and Lye."
Last year, self-serve technology was fitted during a revamp of the Cradley building.
The machine allows visitors to borrow and return books themselves and is also designed to free up staff time so they can focus on helping people in the libraries.
A £208,000 revamp of Dudley Library was also completed. It was given a new layout, carpets, shelving and furniture. A Dudley company was used to carry out the work, which blended in the new shelving with the features of the listed building.
Meanwhile, children and young people visiting libraries in the borough are being asked to take part in a survey which will help design services in the future. It will run from October 21 for two weeks.
Councillor Turner said: "It's really important that children and young people have the opportunity to tell us what they like or dislike about their library to ensure we deliver a library service that is in tune with what they want."
While Cradley library is closed, people can call 01384 812980 to renew books.