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.
THE NEWS9 hours ago
BREAKING: UNILAG governing council sacks vice chancellor
THE NATION3 days ago
‘Yahoo Yahoo’ boys have become role models – Ex-minister, Diezani
THE NEWS18 hours ago
You’ve failed, you deceived Nigerians with fake promises – Catholic bishops lambast Buhari
THE NATION16 hours ago
Another Lagos LG chairman dies of COVID-19 complications
THE NEWS6 hours ago
Ignore council’s statement, I remain UNILAG VC – Ogundipe
THE NEWS2 days ago
JAMB to higher institutions: Start 2020/2021 admission processes
THE NEWS2 hours ago
DSS releases ex-CBN deputy gov, Mailafia, after six-hour grill
SPORTS2 days ago
Doodo: The Nigerian teen sports analyst making waves