UEFA, the governing body of European soccer, issued the fine after the Sands banner and another featuring Scottish national icon William Wallace were unfurled by Celtic fans at their home game with AC Milan in November.
It is the fourth fine Celtic has received in recent years for ‘inappropriate’ gestures by their fans, many who have an Irish background.
The fine was issued after a group of fans known as the Green Brigade displayed their Bobby Sands banner.
The Belfast Telegraph reports that UEFA’s control and disciplinary body found the club guilty of allowing an ‘illicit banner’ to be displayed at the game with Milan on November 26.
A set of lyrics was also displayed which included the line: ‘The terrorist or the dreamer?’
UEFA’s announcement reaffirmed that its rules prohibit messages of a political and ideological nature being displayed in a stadium.
In response, Celtic released a statement which said: “Clearly it is extremely disappointing that the club must pay another sizeable penalty following the actions of a small minority, particularly given the previous assurances which were made to the club and the widespread understanding of the likely outcome of such actions.
“Regrettably, due to previous charges being brought against the club, again following the actions of a small minority, the fines imposed by UEFA are increasing in scale.
“It goes without saying that such actions must stop now, before the club receives a competitive sanction or one which would affect our supporters attending European matches.
“We are Celtic supporters and we must now move on. We are sure our fans will come together, unite with the club and support the team with the commitment and passion we are famous for, ensuring that Celtic Park once again provides a positive footballing occasion for all.”
Celtic is actively trying to disband the Green Brigade following recent scenes at Motherwell when Celtic fans broke up a section of the stand during a Scottish league game.
The club has handed ‘precautionary suspensions’ to 128 supporters preventing them from attending home or away games.
Another 250 season ticket-holders based in section 111 - the ultras’ corner of Celtic Park - will be moved to other parts of the ground or given refunds on season tickets.
The Green Brigade has said that its banners at the Milan game were football-related and designed to protest against the Scottish Government’s Offensive Behaviour at Football Act and the Scottish Police's implementation of the legislation, which it claims has criminalised expressions of Irish politics.
Celtic boss Neil Lennon admitted his ‘heart sank’ when he saw the display, arguing it was neither the time nor place for such a demonstration.
Celtic was also fined two years ago after supporters chanted pro-IRA slogans during a Europa League match in France.