Laidlaw has been ruled out for the remainder of the campaign after damaging ankle ligaments during his side's defeat to France last time out, while Josh Strauss and Sean Maitland also miss the game through injury.
Allan Dell and Hamish Watson drop to the bench as head coach Vern Cotter makes five changes to his starting XV, with Ali Price, Ryan Wilson, Tim Visser, Gordon Reid and John Hardie all coming into the side.
Barclay had been a doubt himself after forced off against France with suspected concussion, but he has recovered and will lead his country out for the second time in his career on Saturday.
"John has played a vital role in our leadership group and has led by example throughout this and previous campaigns. It was disappointing to lose Greig, however we continue to develop a system of shared leadership in this squad, which has supported this transition. It'll be a proud moment for John and one which he thoroughly deserves," Cotter told reporters.
"We've now had two weeks to recover, reflect and prepare a new game plan for Wales. We know the Welsh will throw everything at us but we will keep our attacking mindset and look to convert pressure to points as often as possible.
"The players have worked hard to prepare for this game and are really looking forward to putting in a top performance. It's a huge weekend in the championship and we're still right in the mix."
Scotland and Wales have both won one and lost one so far in this year's tournament.
Scotland team to face Wales: Hogg (Glasgow), Seymour (Glasgow), Jones (Stormers), Dunbar (Glasgow), Visser (Harlequins), Russell (Glasgow), Price (Glasgow); Reid (Glasgow), Brown (Glasgow), Fagerson (Glasgow), R Gray (Toulouse), J Gray (Glasgow), Barclay (Scarlets, capt), Hardie (Edinburgh), Wilson (Glasgow)
Replacements: Ford (Edinburgh); Dell (Edinburgh), Berghan (Edinburgh), Swinson (Glasgow), Watson (Edinburgh), Pyrgos (Glasgow), Weir (Edinburgh), Bennett (Glasgow)