Former Dagenham and Dartford defender Arber, whose father Bobby has also worked for the Gunners as a scout, posted a Tweet on his personal account, @1Arbs, on Monday that suggested he had bet on midfielder Ozil's impending move to the Emirates Stadium.
"Lovely bit of 14-1 Mesut," he wrote.
The Premier League club confirmed on Friday they were treating the Tweet as a matter of urgency and by the afternoon they announced they had reached a conclusion.
"We take this very seriously," a club spokesman said.
"All Arsenal employees and workers are well aware of their responsibilities in this respect. Following an investigation we have taken appropriate action in relation to a casual worker."
The Football Association declined to comment when contacted but, if Arber had bet of the arrival of 24-year-old Ozil, who completed a club-record £43million move from Real Madrid late on transfer deadline day, the 35-year-old is likely to have broken terms highlighted in the FA's guide to betting rules.
The rules state: "You are not allowed to place a bet on a game or competition in which you have any influence, either direct or indirect.
"The above includes all bets related to the following: Any other events involving your club or other clubs playing in the same league competition (such as next manager markets)."