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,” said Spaniard Arteta, 37. “I will be at work as soon as I’m allowed.”
Arsenal expects a “significant number of people” will self-isolate, including the “full first-team squad”.
BBC Sport understands all 20 Premier League clubs want to decide on a unified strategy, and one of the possible options that will be discussed at the meeting is postponing all 10 of this weekend’s scheduled fixtures.
“The health of our people and the wider public is our priority and that is where our focus is,” said Arsenal 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).
Arsenal’s Premier League match with Manchester City on Wednesday was postponed as a “precautionary measure” and several Gunners players went into self-isolation after Olympiakos owner Evangelos Marinakis contracted coronavirus.
Arsenal said Marinakis, 52, met a number of their players when the Gunners hosted the Greek side in a Europa League match two weeks ago.