The Gunners have closed their training ground and club staff who had recent contact with Arteta will now self-isolate.
The club expects it to be a “significant number of people”, including first-team staff and coaches.
In a statement, Arsenal managing director Vinai Venkatesham said Spaniard Arteta, 37, was “disappointed but in good spirits”.
“The health of our people and the wider public is our priority and that is where our focus is,” he added.
“We are in active dialogue with all the relevant people to manage this situation appropriately, and we look forward to getting back to training and playing as soon as medical advice allows.”
Arsenal are due to play at Brighton in the Premier League on Saturday (15:00 GMT).
Earlier on Thursday, the Premier League said games “will go ahead as scheduled” despite the coronavirus outbreak.
Manchester City defender Benjamin Mendy is self-isolating as a precaution after a member of his family was admitted to hospital displaying symptoms of coronavirus.
Three Leicester City first-team players have also self-isolated after showing symptoms of coronavirus.