Matt takes the place of Gordon McIlwham who has been promoted to the starting XV in place of the injured Gavin Kerr.
"I'm very surprised, but I'm coming into the squad to do a job, and if I get an opportunity I'm going to grab it with both hands," said Matt.
Lee Harrison has been recalled to Glasgow's starting XV for the Celtic League match against Cardiff at Hughenden this evening (ko 7.30pm).
Andy Kelly takes Harrison's place among Glasgow's substitutes.