The other changes to the team which beat Bath 37-10 last weekend see Finn Russell replace Duncan Weir at fly-half and Tim Swinson come in for Leone Nakarawa at second row, to make his 50th appearance for the club.
The last time the two teams met in France was in 2011, when the sides drew 13-13, with Rory Lamont scoring the Warriors try that day.
Glasgow have an unchanged back three, with Stuart Hogg operating at full-back and Tommy Seymour and Sean Maitland on either wing.
Dunbar returns from injury at centre in place of Peter Horne and lines up alongside Mark Bennett, who scored two tries against Bath in the last round.
Russell starts at stand-off and last week’s man of the match Henry Pyrgos is at scrum-half.
In the pack, Gordon Reid and Euan Murray make their third consecutive starts, while centurion Pat MacArthur is retained at hooker.
Jonny Gray and Swinson will be in charge of the engine room and Strauss comes in at number 8, replacing Adam Ashe.
The South African, who will combine with Rob Harley and Chris Fusaro in the back-row, will captain the side.
Fraser Brown and Alex Allan are the only changes to the bench from last week, with Dougie Hall and Jerry Yanuyanutawa not included in the squad.
Glasgow Warriors head coach Gregor Townsend said: “Our win against Bath has given us the best possible start to our European campaign and we are very determined to build on that result over in France.
“Montpellier have been in great form this season and they have a squad packed full of international players. We are looking forward to the challenge of playing in France against a quality side.
“It’ll be a special day for Tim Swinson, who is set to make his 50th appearance for the club and I’d like to congratulate him on this achievement.”
Glasgow Warriors team to play Montpellier
15. Stuart Hogg
14. Sean Maitland
13. Mark Bennett
12. Alex Dunbar
11. Tommy Seymour
10. Finn Russell
9. Henry Pyrgos
1. Gordon Reid
2. Pat MacArthur
3. Euan Murray
4. Tim Swinson
5. Jonny Gray
6. Rob Harley
7. Chris Fusaro
8. Josh Strauss (Captain)
16. Fraser Brown
17. Alex Allan
18. Rossouw de Klerk
19. Leone Nakarawa
20. Adam Ashe
21. Niko Matawalu
22. Duncan Weir
23. DTH van der Merwe
Not available due to injury: Mike Cusack (medical / illness), Ryan Grant (shoulder), Tyrone Holmes (neck / shoulder), Tom Ryder (neck) and Ryan Wilson (ribs).