Before Friday's Scottish Premiership match, a flare was lit in the Celtic end before a green smoke bomb was thrown on the pitch.
After Kris Commons scored the first goal in Celtic's 5-0 win, a missile thrown from the away support flew over Hoops goalkeeper Fraser Forster's head and play was quickly halted after Motherwell restarted when a green smoke bomb went off on his goal-line.
After the match, it became apparent that dozens of seats had been broken in the middle-lower section of the South Stand, just above where a Green Brigade banner had been displayed on the front of the stand.
A statement from Celtic read: "Clearly we are appalled by the scenes from last night's match and the actions of a small minority which have again tarnished the great reputation of the club and our supporters on a night when our team produced such a fantastic performance.
"We are currently investigating these events and will update our supporters early next week."
The pyrotechnic displays came days after the Scottish Football Association launched investigations into similar incidents at William Hill Scottish Cup ties the previous weekend.
A flare thrown from the Rangers support after their win at Falkirk damaged the pitch and a smoke bomb was thrown from the Motherwell support on to the New Douglas Park surface during their defeat by Albion Rovers.
Celtic manager Neil Lennon hit out at the latest incidents after the game.
He told BBC Scotland: "It is unnecessary. I don't see what they bring to the game.
"It's at our end with our goalkeeper there and it's always a worry that by accident someone could get hit or something could get damaged by it.
"I don't see what the turn-on is with it - it does nothing for me. I just don't see what they add to the atmosphere of the game."
Celtic are set to foot the bill under a reciprocal agreement between clubs but could also find themselves facing a Scottish Professional Football League investigation once the league studies its delegate report.
Meanwhile, a Police Scotland spokeswoman said: "During the course of the match, 18 smoke bombs, three fireworks, and one flare were set off.
"Significant damage was caused to seats within the ground and we are looking into this matter along with the club to establish the circumstances.
"There were no arrests made inside the ground."