Gardai - the police force of the Republic of Ireland - and stadium officials are studying CCTV footage in an attempt to identify a spectator alleged to have thrown the missile onto the pitch during the Barclays Premier League club's 4-0 victory at Thomond Park on Sunday.
A statement released on behalf of Limerick FC and Thomond Park Stadium said: "The Gardai and stadium officials are reviewing the CCTV recordings to attempt to identify an individual involved in the throwing of an offensive object onto the playing field."
It continued: "Any individual identified as being involved in an incident of this nature will be banned from future attendance and the matter will be handed over to the Gardai.
"All those involved with the friendly game fully condemn all forms of unacceptable behaviour of this nature."
It is understood Manchester City made no formal complaint over the incident, which was mentioned by Clichy via his Twitter account.
He tweeted: "How sad to see 'bananas thrown on the pitch' tonight... Knowing people around the world need food. #nowordsforthis."