The 22-year-old will miss out as his side face Russia on October 10 and San Marino three days later as they look to revive their faltering qualification campaign.
Tierney has been introduced into the fold for the Gunners slowly as he continues his recovery from a double hernia operation in the off-season.
Following his Gunners debut, Tierney was not in the squad on Monday as Arsenal drew Manchester United 1-1 at Old Trafford.
Scotland manager Steve Clarke indicated at a press conference that he left the young defender out of his squad at the request of Arsenal.
"I was close to selecting Kieran, obviously Arsenal have indicated to us that they'd prefer us not to select him at this moment in time because he's only played 70-odd minutes of football and you have to respect the club's decision on that," Clarke said.
"I'd like to get Kieran in the squad and have him as part of the group but at this moment in time it's more important that Kieran gets minutes on the pitch, gets himself back to full speed and when that happens I'm sure he'll be a valuable member of the squad."
Tierney joined Arsenal from Celtic for £25 million ($31m) on deadline day, and the Gunners are looking to be extra cautious with their new signing.
Following his debut last week, his defensive team-mate Rob Holding said he was impressed with the young Scot's performance.
“I think he was brilliant,” Holding said of Tierney.
“I loved having him on the left side of me. He was solid and for his first game back from a double hernia operation you can't ask for any more than that.”
After their game at Old Trafford the Gunners face a quick turnaround, with a Europa League fixture against Standard Liege set for Thursday.
Following that match Arsenal are back in action in the Premier League on Sunday as they host Bournemouth.