In a strongly-worded statement on the club's website (www.celticfc.net), Celtic said they were working with Glasgow City Council's Safety Advisory Group over serious safety concerns in the stadium.
Celtic said they had considered closing down Section 111 of the stadium - the area where the ultras group known as the 'Green Brigade' are situated - but that it would remain open for a friendly against Borussia Moenchengladbach on Saturday.
Among the disturbances noted by the Safety Advisory Group were "moshing" - mock fighting/jostling - which caused damage to 131 seats, body surfing and the refusal of supporters to comply with directions from stewards.
Three fireworks were ignited in Section 111.
"The Club is keen to work with spectators in Section 111 to resolve safety concerns," the club said. "However, it should be understood that failure to stop this unsafe behaviour will require the closure of this area in Celtic Park.
"The Directors and Board of Celtic Football Club consider their responsibilities with regard to Spectator Safety to be of paramount importance.
"We will continue dialogue with representative of fans in this area to resolve these serious safety concerns, however this unsafe behaviour must stop."
Celtic were fined 25,000 euros (£21,461.45) for the misbehaviour of their fans during a Europa League game against Udinese in Italy in December, 2011.
UEFA will deal with the case on August 22.
(Reporting by Martyn Herman; editing by Ken Ferris)
