Photographs show Stone on the big screen at Tynecastle stadium before last night’s SPFL match between Hearts and Celtic.
It appears Hearts were duped after issuing a request for supporters’ pics ahead of kick-off.
Today the club said its fans’ social service had been “abused”.
Several photos of the incident are circulating online.
A user, whose account appears to have been deleted, had replied to a request on X from Hearts for fan messages.
They posted: “My mate michaels (sic) first game in years, here’s a old photo of him coming through the turnstiles”.
The message was accompanied by an old snap of Stone, taken in 1998 as he left the Maze Prison on temporary Christmas release.
Stone killed three people in a gun and grenade attack at Milltown Cemetery in west Belfast following an IRA funeral in 1988.
Catholic civilians Thomas McErlean (20) and John Murray (26), and IRA member Caoimhín Mac Brádaigh (30), were killed. Around 60 others were injured.
Stone managed to flee a crowd of mourners who pursued him but was apprehended by RUC officers.
He was also convicted of three other killings: milkman Patrick Brady in south Belfast in 1984; joiner Kevin McPolin in Lisburn in 1985 and bread delivery driver Dermott Hackett near Omagh in 1987
After being freed in 2000 under the terms of the Good Friday Agreement, Stone was sent back to prison after entering Stormont in 2006 armed with explosives and an axe in an attempt to murder Gerry Adams and Martin McGuinness.
He was released from prison on parole in January 2021.
Hearts have apologised and pledged to review their procedures.
A spokesperson said: “Our fans’ social service was abused by someone online, leading to an image appearing on the stadium’s big screens, and we apologise for any offence caused.
“We will review our procedures internally to ensure this type of misuse is not repeated.”
Celtic won the match 4-1 to move three points clear at the top of the Scottish Premiership table.
After a goalless first 45 minutes at Tynecastle, quickfire goals from Kyogo Furuhashi and Nicolas Kuhn in the second half put Celtic in control. Adam Idah scored twice, with Musa Drammeh on target for Hearts.
Last year, Championship club Bristol City apologised after a similar incident involving Stone at its Ashton Gate stadium.
During the club’s home game against Burnley, a message appeared on the screen which read: “Congratulations Michael Stone for beating Milltown 3-0 in the cup final. From dad.”
The club promised to conduct a review and said the message “should never have got through our checking procedures”.