The Wales Under-20 ace has featured off the bench in two league games for Cardiff Blues this season, but Smith is now handed a starting spot at the Scotstoun Stadium.
The coaching team of Paul John and Dale McIntosh make a total of seven changes to the starting line-up from the European side.
Tom Isaacs will line-up alongside Smith in midfield while a new-look half back pairing of Gareth Davies and Tavis Knoyle will start the game,
Positional changes see Gareth Anscombe play at full back while Dan Fish switches to the wing.
A new front row combination will see Sam Hobbs, Kristian Dacey and Adam Jones pack down while Macauley Cook is called into the back row alongside skipper Sam Warburton and Josh Navidi.
Lucas Amorosino, Joaquin Tuculet, Rhys Patchell, Lloyd Williams, Cory Allen, Manoa Vosawai, Filo Paulo and Gethin Jenkins are among those that miss the game due to injury.
Coach Paul John has called on Cardiff Blues to respond in the right manner to European defeat last weekend and insists they can play without fear in Scotland.
“We’ve got to start to rebuild and finish the season with pride,” he said. “We have the chance to look at a few players over the coming games who will play a big part in the first few months of next season due to the Rugby World Cup.
“People will get an opportunity to show what they can do. In the next few weeks we will look at our options and it’s an exciting time for some of our younger players, and in this instance Garyn, to really put their hands up.
“We won last year at Glasgow in Europe and we’ve got absolutely nothing to lose,” he added.
“We want to play to a game plan, execute it well and perform to the best of our ability. To do justice to the league we have to do that.
“Glasgow are a good offloading side, they are a complete side in many ways, and we’ve got to control the ball better than we did last weekend against Newport to get the right performance.”
Cardiff Blues: 15 Gareth Anscombe, 14 Alex Cuthbert, 13 Tom Isaacs, 12 Garyn Smith, 11 Dan Fish, 10 Gareth Davies, 9 Tavis Knoyle; 1 Sam Hobbs, 2 Kristian Dacey, 3 Adam Jones, 4 Jarrad Hoeata, 5 Lou Reed, 6 Macauley Cook, 7 Sam Warburton (c), 8 Josh Navidi
Replacements: 16 Matthew Rees, 17 Thomas Davies, 18 Taufa’ao Filise, 19 Josh Turnbull, 20 Ellis Jenkins, 21 Lewis Jones, 22 Simon Humberstone, 23 Richard Smith