With the country in lockdown, Aubameyang was filmed posing with a new tattoo alongside a tattoo artist.
Arsenal investigated the incident to find out if lockdown rules had been breached but kept their findings in-house, with Arteta saying: 'Whatever we do with our players we keep it internally.
'It is true that there are a lot of members of our squad that have extended families at home and if any player does something that is not in the regulation obviously the club acts immediately - but always privately as well.'
Aubameyang was left on the bench for the north London derby due to lateness.
'He was going to start the game,' Arteta told Sky Sports. 'We had a disciplinary issue. We have drawn the line and we move on. He is on the bench.
'We have a process we have to respect for every game and that is it. We have a way of leaving together that we have to respect each other and that is it.
'But he is an incredible guy and he is one of the most important players in the team, he is our captain, and we move forward.'
Arsenal won the game 2-1, with Aubameyang an unused substitute.
Having returned late from a pre-approved trip to France to visit his ill mother, Aubameyang has lost the captian's armband at Arsenal and his future has been thrown into major doubt.
In a curt statement on Tuesday, Arsenal said: 'Following his latest disciplinary breach last week, Pierre-Emerick Aubameyang will no longer be our club captain, and will not be considered for selection for Wednesday's match against West Ham United.
'We expect all our players, particularly our captain, to work to the rules and standards we have all set and agreed. We are fully focused on tomorrow's match.'
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