The nearest alternative is Finchfield Library, White Oak Drive, which will be open from 10am-1pm and 2pm-7pm.
Tettenhall Library is expected to be open as normal on Friday.
Councillor Jasbir Jaspal, cabinet member for public health and wellbeing, said: "Although this is due to circumstances beyond our control, we apologise in advance for any inconvenience the temporary closure of Tettenhall Library on Thursday may cause.
"It should reopen as normal on Friday but customers are reminded that their membership enables them to use Finchfield Library or indeed any other library in the city.”
For more information about how to join libraries for free visit wolverhampton.gov.uk/libraries.