Aberdeen say the players who broke lockdown rules have been "severely reprimanded and fined heavily", with the money donated to NHS Grampian.
Eight first-team members have already apologised for a "huge error of judgement" after a visit to a busy bar.
Two tested positive for Covid-19 and three of Aberdeen's matches have been postponed as a result.
"They are in no doubt that they have let themselves and the club down," said chairman Dave Cormack.
The eight players are Bruce Anderson, Craig Bryson, Sam Cosgrove, Michael Devlin, Jonny Hayes, Matty Kennedy, Dylan McGeouch and Scott McKenna.
With the club's internal investigation into the matter concluded, Cormack added that the fines, while confidential, are "in line with the severity of the consequences of their actions".
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"Their actions were indefensible but the investigation has been completed, they have apologised, they have been punished by the club, and are suffering the humiliation that goes with making a mistake in the public eye," he said in a statement.
"The club, like every employer, has a duty of care to its staff and we must also consider the wellbeing of these players, who continue to face an ongoing barrage of criticism and personal abuse from many quarters.
"They've been taught the harshest of lessons and have the chance to redeem themselves and help demonstrate that the club is better and bigger than this regrettable episode."