Regular skipper Scott Brown was suspended for the Scottish Cup second-round clash with Kilmarnock, which the Bhoys won 5-0 with Tierney scoring a spectacular goal from distance.
The 20-year-old Scotland international has impressed all at the club with his talent and poise on the pitch and has been branded as a captain in waiting by Celts coach Brendan Rodgers.
The Isle of Man-born stopper admitted his delight at wearing the armband but is prepared to bide his time and learn under the current captain.
"It was a real honour for me to captain the team," he said. "Broony was obviously suspended for the game but I felt the whole team did well. From the first whistle until the last, everyone was great.
"I think if you asked every Celtic fan in the world 'would you like to captain the team?'' then I think they'd all say they would.
"That's the obvious answer. But Broony is here for a good few years yet."