Fagerson has been ruled out for around eight weeks after picking up a foot injury while training with Warriors on Thursday.
Cummings is also out for around eight weeks having damaged a hand in training this week while Gibbins will be out of action for twelve weeks having undergone surgery on an Achilles injury.
Meanwhile, Fraser Brown will see a specialist after suffering a series of head injuries this season.
The hooker is sidelined indefinitely, with Glasgow coach Dave Rennie pledging to "leave him out until we know a bit more".
Speaking to the press ahead of Glasgow's visit to Italy, Rennie said: "Zander could be out for eight-plus weeks. A bench landed on his foot yesterday and, because he's got to push in scrums, the load that goes through that. Hopefully eight weeks.
"Six Nations is a pretty exciting time for young men, so Zander will certainly miss out on that."
Brown has suffered several head injuries this season, including during Scotland's autumn hammering of Australia, and most recently in Glasgow's victory over Edinburgh on Saturday.
"Fraser is an odd one," Rennie added. "He gets a knock around the jaw [against Edinburgh], bounces back with no symptoms, so he'll test and he'll be able to get through all the [return-to-play] protocols and be available.
"He's done all that this week, but we're at the stage where we want to dig a little bit deeper.
"So he'll go down and see a specialist next week and we'll find out why this is happening.
"We'll basically leave him out of footy until we know a bit more."