The library will close on September 24. It will be replaced with a mobile service, which will run in the village hall car park, starting on October 4.
It will run on Tuesdays, from 11.30am to 12.30pm, and on Fridays, from 9.30am to 10.30am.
The closure of the library was confirmed by Shropshire Council's cabinet following a period of consultation.
Shawbury Parish Council said it could not afford to keep the village library open as it would have cost it about half of its budget.
The unitary authority's cabinet also confirmed plans to cut a total of 57 opening hours across 11 of the county's libraries.
Bridgnorth Library will see a reduction of 11 and a half hours, Ludlow – six hours, Market Drayton – five and a half hours, Oswestry – eight hours, Shrewsbury will see a reduction of eight and a half hours, Whitchurch – three hours, Bayston Hill – two and a half hours, Gobowen – two hours, Much Wenlock – two hours, Shrewsbury, The Lantern – three hours, and Wem – five hours.
Councillor Stuart West, Shropshire Council's cabinet member responsible for libraries, said that the move would ensure that libraries could remain open.