The incident occurred shortly after Ryan Christie had netted the away side’s second goal in the 2-0 triumph.
Both Neil Lennon and St Mirren boss Oran Kearney expressed their disgust in the aftermath, with the latter saying he was tempted to take his team off the field.
This is the latest in a long line of incidents involving fan misbehaviour at matches and Celtic have vowed to do all that they can to tackle the problem.
They said in a statement: “Celtic Football Club today announced that it is carrying out a full investigation into last night’s events at St Mirren Park in an attempt to identify those who are responsible. The club will take the strongest action possible should it be able to identify anyone involved.”
Chief executive Peter Lawwell was then quoted as saying: “Last night’s incident was completely unacceptable and not something we ever want to see repeated. The safety of everyone in football - players, fans, staff, and officials - should always be our priority and, collectively, we need to do all we can to ensure this remains the case.
“There have a been a number of incidents across many clubs this season, with a range of items, including pyrotechnics, being thrown on to pitches. We need to do all we can to remove this from our game.
“From a Celtic perspective, the club does not want it, our players do not want it, our manager does not want it and our supporters do not want it.
“There are serious safety concerns associated with such behaviour, and regardless of the obvious reputational damage which this kind of behaviour has on the club, there are numerous potential repercussions which could have hugely detrimental consequences for the club and our supporters.
He added: “Our supporters are fantastic and we greatly value their contribution. It is the positive support of our fans this season which has helped us deliver one trophy this season and a 13-point lead in the Scottish Premiership. We achieved another excellent away win last night and our on-field success should be the real talking point.
“This kind of behaviour, indeed any form of unacceptable conduct, only serves to tarnish the reputation of the club and our own fans. We need to all work together to make sure this stops now.”