The club has closed its training ground and any staff or players who have been in recent contact with Arteta will now self-isolate.
Arsenal say they expect this to be a “significant number of people”.
“The health of our people and the wider public is our priority and that is where our focus is,” said Gunners managing director Vinai Venkatesham in a statement.
“Our thoughts are with Mikel who is disappointed but in good spirits. 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 scheduled to play away at Brighton on Saturday.
The Premier League announced earlier on Thursday that all of this weekend’s matches would go ahead as normal, but clubs will now hold an emergency meeting on Friday morning.
Fixtures in the top flights of Spain, Portugal, the Netherlands and the USA have all been suspended in an effort to limit the spread of the virus.