Arber appeared to admit betting on Mesut Ozil's transfer to Arsenal on transfer deadline day, posting on his personal Twitter account: "Lovely bit of 14-1 Mesut."
His comments suggest that he had put money on Arsenal being the club of Ozil's choice, which would constitute a breach of Football Association betting rules.
FA rules state that: "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)."
Arsenal said on Friday that the matter had been investigated, and a conclusion had been reached.
"We take this very seriously," an Arsenal spokesman said.
"Following an investigation we have taken appropriate action in relation to a casual worker.
"All Arsenal employees and workers are well aware of their responsibilities in this respect."
Ozil joined Arsenal from Real Madrid for a reported fee of £42.5million on Monday.
Arber, 35, started his career at Tottenham but moved on to Barnet without making a first-team appearance. He also counts Peterborough United and Dagenham & Redbridge among his former clubs.
As well as coaching at Arsenal, he now plays for non-league Corby Town.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
