Michael Owen, the vice-captain, will take over captaincy duties against Ireland with Stephen Jones installed as his deputy. Thomas will be replaced at full-back by the Scarlets' Lee Byrne. Dafydd James, also with the Scarlets, comes in for Williams in a straight swap on the wing.
"Lee (Byrne) is a natural replacement for Gareth at full-back and he has performed well already in that position both in the Autumn and when required against England and Scotland this season," said Johnson. "Daf (James) had an exceptional Autumn series and has been unlucky not to figure so far during the RBS Six Nations, but the injury to Shane gives him his chance. He is in top form at the moment and we are lucky to have such an experienced player to call into the team."
Johnson has also made three changes on the bench with Ospreys pair Jonathan Thomas, returning from injury for Adam M Jones, and Gavin Henson, returning from a ban to replace Nicky Robinson, and the Scarlets' Barry Davies providing cover for full-back after Byrne is moved to the starting XV.
"Jonathan and Gavin both figured for the Ospreys last weekend and acquitted themselves well. Jonathan offers us versatility covering both the back and second row from the bench and Gavin is covering both the fly-half and inside centre position, which is especially important to us in the absence of Alfie and Ceri Sweeney.
"Apart from the enforced changes we have gone for continuity in selection, which is logical when you realise that all the present coaches have been part of previous selection panels."
Wales's record in Ireland in the RBS Six Nations Championship registers just one win, in 1999, but Johnson believes the events of recent weeks in the Wales camp can only make the team stronger and he plans to makes Welsh fans proud this weekend.
"Tough times breed tough men and we are taking a tough team to Dublin to play tough rugby," added Johnson. "We are going to look squarely in the face of adversity and show a different side to our characters this weekend. We've shown that we can turn on the pretty stuff, now we are going to show our true heart, make Welsh fans proud of us and proud to be Welsh and come out fighting."