The forward suffered the damage during the Warriors’ defeat by Leinster in Dublin last Sunday.
Gray has already missed a large chunk of the season for club and country due to concussion and Glasgow are understandably wary about him returning too soon.
The lock has been in fine form in recent weeks and made significant contributions as a substitute in Scotland’s opening two Six Nations fixtures, against England and Wales.
“It is a minor head knock which he is recovering from. He is going through the process,” said Danny Wilson, the Glasgow coach.
“The key with Richie is the history [of head injuries]. With the history he’s got, and with missing a lot of rugby this season with concussion, we have to make sure player welfare is first and foremost and we are not putting someone with a concussion history at any sort of risk.”
Asked if the player could now be considered doubtful for Scotland’s match against Ireland at BT Murrayfield a week on Sunday, Wilson said: “Probably too early to say. There’s a big question mark on that, I would say, because of the recent history – but we’ll have to wait and see.”
Wilson is without international quartet Scott Cummings, Matt Fagerson, Ali Price and George Turner for the Zebre game and the coach was keen to rebuff speculation linking Price with a move to Gloucester.
The Scotland scrum-half has been in outstanding form this season but Glasgow have only seen him fleetingly due to his commitments with the national team and Wilson is anxious that he remains with the club.
“It’s pretty straightforward from our end,” the coach said. “Ali is under contract, he’s under contract next season, and as far as I’m concerned that won’t be changing.
“Rumours are rumours. They fly around from time to time, but Ali has been outstanding in the small amount of rugby he’s had for Glasgow this year.”
In Price’s absence, the up and coming Jamie Dobie will wear the No 9 jersey in Parma.
“I think Jamie is, first and foremost, a really exciting threat. We’ve seen as a rugby player – forget scrum-half for a minute – his evasion, his footwork, his speed and he’s strong as well. Remember, he’s a kid – he’s 19 years old – so I think he’s such an exciting prospect for the future.”
There is also a first start for another teenager, back-rower Gregor Brown, who impressed coming off the bench against Leinster.
With Adam Hastings suspended, Ross Thompson starts at stand-off, with Irish international Ian Keatley among the substitutes.
Wilson, meanwhile, has recruited Peter Murchie as his new assistant coach. The former Glasgow full-back coached Ayrshire Bull in Super6 last season but has been working at Warriors throughout this campaign. He will be deployed primarily as a skills coach.
Glasgow Warriors: Ollie Smith; Rufus McLean, Huw Jones, Sam Johnson, Cole Forbes; Ross Thompson, Jamie Dobie; Oli Kebble, Grant Stewart, Enrique Pieretto, Rob Harley, Hamish Bain, Gregor Brown, Thomas Gordon, Ryan Wilson (c).
Replacements: Johnny Matthews, Dylan Evans, D’arcy Rae, James Scott, Leone Nakarawa, Sean Kennedy, Ian Keatley, Nick Grigg.