The Gunners have closed their training ground and club staff who had recent contact with Arteta will now self-isolate.
The Premier League will hold “an emergency club meeting” on Friday to discuss future fixtures.
This is really disappointing but I took the test after feeling poorly.
I will be at work as soon as I’m allowed.
A significant number of people” will self-isolate, including first-team staff and coaches.
The health of our people and the wider public is our priority and that is where our focus is,” said club managing director Vinai Venkatesham.
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).
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.