Several staff at the Lichfield Street Hub in Walsall town centre were notified as being close contacts of a positive Covid-19 case.
The council building will remain closed until at least Tuesday, July 27, as it undergoes a deep clean while staff are self-isolating.
Stephen Gunther, director of public health for Walsall Council, said: "Over the next few days we will endeavour to contact visitors who have been at the library over the past week, although there is no suggestion they will have been in close contact.
“At this current time they do not need to self-isolate unless they are displaying Covid-19 symptoms – a high temperature, new persistent cough, loss of taste or smell – or are contacted by NHS Track and Trace team and told to do so.
"Covid-secure guidelines continue to be in place at Walsall libraries which will ensure there is minimal risk to others as a result of this. This includes regular cleaning, staff protocols such as frequent hand washing and social distancing.”