30-year-old Graeme has already made 176 appearances for the Warriors since joining the club in 2003 from Glasgow Hawks.
The team will wear a special commemorative badge on their shirts for the game.
Glasgow Warriors head coach Gregor Townsend said: "This is a massive game for the club and it will also be an opportunity for the supporters to celebrate Graeme's incredible ten years here.
"He is a fantastic ambassador for the club and the standard of play he has delivered over the years is a great credit to him."
It is the final home game of the regular season at Scotstoun Stadium (ko7.35pm) and Glasgow can secure a play-off place with a win against the defending champions.
Tickets can be bought online at www.glasgowwarriors.org and over the phone by calling 0844 800 3490 (9:00am-5:00pm Mon-Fri).