Stuart McInally will skipper the side in Laidlaw’s absence from the starting XV while there is a first start for McInally’s Edinburgh team-mate Darcy Graham, who comes in for the injured Sean Maitland on the wing.
The 21-year-old joins Tommy Seymour - making his 50th Scotland appearance - and club colleague Blair Kinghorn in the back-three.
McInally is joined by the returning Willem Nel, who comes in at tighthead after recovering from a calf injury, and loosehead Allan Dell in an all-Capital front-row.
Finn Russell also returns from a head injury to start at stand-off, joining former Glasgow Warriors team-mate Ali Price at scrum-half, which in turn sees Laidlaw move to the bench.
The return of the Racing 92 man sees Pete Horne move to inside-centre in place of Sam Johnson where he partners Scotstoun colleague Nick Grigg.
Townsend has selected an unchanged back-five, with Grant Gilchrist partnering Jonny Gray - also making his 50th Scotland appearance, just days before his 25th birthday - in the second-row while Magnus Bradbury, Jamie Ritchie and Josh Strauss retain their back-row places.
There are three changes among the replacements, with back-row Hamish Watson, loosehead prop Gordon Reid and utility back Byron McGuigan all in with a chance of featuring for the first time this campaign.
Speaking about his team selection, Townsend said: “While there have been some strong moments in our games this campaign, we have yet to deliver that quality and focus for 80 minutes and play to our potential.
“We have had a couple of weeks since our defeat in Paris to look at ways we can improve our performances, through what we do in training, our tactical approach and through selection.
“First and foremost, we select a team we believe gives us the best chance of winning at the weekend, while we also have an opportunity to reward players who have been in very good form and have been knocking at the door of the team in recent weeks – Darcy Graham and Ali Price especially.
“Greig [Laidlaw], having started in our last six games is a key member of our squad, although this week we have decided to utilise his leadership and experience off the bench. He is driven by a desire to win for his country and he should have an important role to play in the latter stages of the match at the weekend.”
Townsend also paid tribute to Gray and Seymour ahead of their 50th caps, with the former becoming the second-youngest Scot in history to reach the milestone.
He added: “Getting to 50 caps for your country is a milestone in a player’s career and it underlines the consistency and quality both Tommy and Jonny have delivered for Scotland over the years.”
Wales arrive in the Capital as the only unbeaten team in the championship, while they have won ten of their last 11 Tests against the Scots. The sole defeat came in the last meeting at BT Murrayfield two years ago.
Townsend continued: “Wales have a very good record against us and are in excellent form. It’s a similar challenge to the one we faced last year against England, who had also been on a very good run of results in their preceding games.
“We rose that the challenge that day and found a way to win and I firmly believe we can reach that level of performance once again on Saturday.”
Scotland team to play Wales at BT Murrayfield Stadium, Saturday 9 March (kick-off 2.15pm) – live on BBC
15. Blair Kinghorn (Edinburgh) – 10 caps
14. Tommy Seymour (Glasgow Warriors) – 49 caps
13. Nick Grigg (Glasgow Warriors) – 7 caps
12. Pete Horne (Glasgow Warriors) – 40 caps
11. Darcy Graham (Edinburgh) – 2 caps
10. Finn Russell (Racing 92) - 42 caps
9. Ali Price (Glasgow Warriors) – 22 caps
1. Allan Dell (Edinburgh) – 20 caps
2. Stuart McInally (Edinburgh) – 25 caps
3. Willem Nel (Edinburgh) – 27 caps
4. Grant Gilchrist (Edinburgh) – 31 caps
5. Jonny Gray (Glasgow Warriors) – 49 caps
6. Magnus Bradbury (Edinburgh) – 5 caps
7. Jamie Ritchie (Edinburgh) – 9 caps
8. Josh Strauss (Sale Sharks) – 20 caps
16. Fraser Brown (Glasgow Warriors) – 40 caps
17. Gordon Reid (London Irish) – 33 caps
18. Simon Berghan (Edinburgh) – 17 caps
19. Ben Toolis (Edinburgh) – 16 caps
20. Hamish Watson (Edinburgh) – 23 caps
21. Greig Laidlaw (Clermont Auvergne) – 69 caps
22. Adam Hastings (Glasgow Warriors) – 9 caps
23. Byron McGuigan (Sale Sharks) – 6 caps