Police noted the singing in the 0-0 draw with Hibernian in October, with the league since announcing that they are confident the club has taken measures to avoid such 'unacceptable conduct' in the future.
The decision was revealed three days before a Uefa hearing following a similar accusation made after the Europa League clash with Rennes on the 3rd of November at Celtic Park.
The SPL released a statement which also disclosed the police match commander had noted 'unacceptable conduct amongst a small number of Celtic fans in that they chanted and sang in support of the IRA.'
The statement added: “Such reports result in an investigation to determine whether any breach of SPL rules by the club in question may have occurred.
“It is not disputed that a small number of Celtic fans engaged in singing and chanting in support of the IRA. Such behaviour is unacceptable and unwelcome at SPL matches.
“It is noted that Celtic FC has condemned such activity publicly on many occasions (most recently by chief executive Peter Lawwell and by head coach Neil Lennon).
“It is important that such public condemnation should continue.
“It has been established through the above investigation that Celtic FC took all reasonably practicable steps before, during and after the match (in consultation and conjunction with Strathclyde Police) to minimise the likelihood of unacceptable conduct occurring and, where it did occur, to assist in the identification and prosecution of offenders.
“The on-going work amongst the club, supporters and police to ensure that any unacceptable conduct is eradicated from Celtic Park is noted and is welcomed.”