Internet servers went down on Tuesday afternoon due to a technical problem and remained offline throughout Wednesday and Thursday including at the historic Shrewsbury Library, on Castle Street.
Libraries in Ellesmere, Ludlow, Shifnal and Market Drayton have also been hit.
A limited internet service was up and running again on public computers by yesterday but customers were still warned to expect disruption.
Officials at Shropshire Council today apologised for the problem and admitted it could take until next week to completely fix the server fault.
It comes little more than two weeks since a massive £25 million broadband deal for Shropshire was signed with BT providing more than 130,000 homes and businesses with access to high-speed internet within the next three years.
Shropshire Libraries tweeted to its 350 followers on Wednesday: "Due to the ongoing major fault on the People's Network, the public computers in all our libraries will not be available again today."
And it added on Thursday: "The public access computers in all our branches will not be available again today. We will have them back up and running as soon as we can."
And a spokesman for Shropshire Council said: "Owing to a technical problem with an internet server, library customers have been unable to access the internet for the last two days.
"It's a major fault and repair work may not be completed until next week. In the meantime, library managers are hoping to provide an internet service from Friday albeit at a limited capacity. We apologise and ask customers to be patient and bear with us until the problem is resolved."
Other libraries affected are Albrighton, Bayston Hill, Bishop's Castle, Bridgnorth, Broseley, Church Stretton, Cleobury Mortimer, Craven Arms, Gobowen, Highley, the Lantern in Shrewsbury, Much Wenlock, Oswestry, Pontesbury, Shawbury, Wem and Whitchurch.