The service, Ready Reads, enables customers to pre-order books and collect them from the library foyer and will be available at Shrewsbury, Oswestry and Ludlow from July 6.
All books will have been quarantined for 72 hours before being issued and customers will then be contacted when their books are ready to collect.
The scheme is set to be rolled out to the other libraries across the county in coming weeks.
While customers cannot request specific titles, people can suggest what subjects and genres they would like and library staff will select books to suit them.
Iran Morris, Ludlow Library manager, said they were planning to open from 10am to 2pm on Monday, Tuesday, Wednesday, and Friday.
He added: "We are really looking forward to welcoming our customers back.
"We will be operating a contactless service from our library foyer where people can both return and collect their books. Social distancing and other safety measures will be in place to make this as safe as possible."
Customers can request up to 10 books at a time which will be issued for six weeks.
This comes as Shropshire's six biggest libraries were open for this week only in order to accept returns of books and other loaned items.
While late fees have been suspended, Shropshire Council confirmed all returned books will enter a period of quarantine before they can be lent out.
Libraries will have a phased opening and to enable social distancing, there will be a limit on the number of people in any library at once.
There will also be a reduced number of computers available for use, based on 30-minute sessions and these must be pre-booked by contacting the library.
Other items which cannot be quarantined or sanitised, such as newspapers, leaflets and some reference materials, will be unavailable until the risk of spreading coronavirus has been reduced.
Books can be ordered by email, over the phone or via the Shropshire Libraries website at shropshire.gov.uk/libraries.
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