The threat was made following disruption caused by fans.
A statement on the football club's website raised issues including overcrowding in Section 111, mock fighting and jostling, known as moshing, and 'body surfing' by young people over the heads of spectators at Tuesday night's match against Cliftonville FC.
The statement said 131 seats were damaged during the game at Celtic Park and three fireworks were also exploded within Section 111 causing the referee to require a stadium announcement to stop such behaviour.
It said: "As a result of this unprecedented step by a match official, Celtic FC will now be the subject of a disciplinary action for contravention of the UEFA Safety and Security Regulations.
"Following the events of last Tuesday's match, the Club's position was to close Section 111, but following discussions between the Club's Supporters' Liaison Officer and representatives of the 'Green Brigade' that decision has been reviewed and the section will remain open.
"However, the situation will be monitored at both the Celtic FC v Borussia Monchengladbach match on Saturday, July 27, and the Celtic FC v IF Elfsborg match on Wednesday, July 31.
"The Club is keen to work with spectators in Section 111 to resolve safety concerns.
"However, it should be understood that failure to stop this unsafe behaviour will require the closure of this area in Celtic Park."
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