Gary O'Driscoll - one of the club's doctors - reportedly took a photo of the sheet, which leaked after he used a file-sharing website.
Fines can be dished out for being late for training, travel and meetings, bringing the wrong kit on match days, and taking phone calls while in the building.
Defender Per Mertesacker is also named on the sheet as the enforcer.
Responding to a question about Mertesacker's role, manager Arsene Wenger joked: "The Germans do well economically and we respect that.
"They are the only ones that make money in Europe. That's why we've chosen a German."