The Scotland lock's year so far has been dogged by injuries.
He missed the Six Nations championship after undergoing surgery on his arm and was back on the operating table over the summer for a procedure on his shoulder and is yet to feature in this year's GUINNESS PRO12.
Kellock last turned out for the Warriors in May's PRO12 final defeat to Leinster, but is set to start at Bridgehaugh Park, alongside Tom Ryder, Sean Maitland and Finn Russell.
"This is an excellent opportunity for a number of players to get valuable game time, at a high level against our nearest rivals, said A team head coach Kenny Murray.
"It's great that the likes of Al Kellock, Tom Ryder, Finn Russell and Sean Maitland will be pulling on a Glasgow shirt for the first time this season.
"We're also delighted that a number of players, both from our EDP [Elite Development Players] system and from the club game, will get an opportunity to show what they can do at this level."
Glasgow have made a storming start to their PRO12 season, with three victories from three against Leinster Rugby, Cardiff Blues and Newport Gwent Dragons.
They welcome in-form Connacht Rugby to Scotstoun Stadium on Friday night.
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