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.
[BREAKING] COVID-19: Nigeria records another eight new cases, toll now 97
The number of Coronavirus (COVID-19) cases in Nigeria hit 97 on Saturday evening with eight fresh cases, says the Nigeria Centre for Disease Control.
“As at 10:40 pm 28th March there are 97 confirmed cases of #COVID19 reported in Nigeria with 1 death,” it stated.
COVID-19: Please, pray for my husband, El-Rufai’s wife begs Nigerians
Hadiza Isma, the wife of the Kaduna State Governor, Mallam Nasir El-Rufai, has appealed to Nigerians to offer prayers for the quick recovery of her husband who tested positive for coronavirus (COVID-19).
She made the appeal a few minutes after her husband disclosed that he tested positive for the virus on Twitter.
THE WITNESS reports that El-Rufai had on Saturday announced that he had been infected with the virus but had no symptoms.
“Dear Tweeps, my husband, the Governor of Kaduna State has tested positive for COVID-19. Please keep us in your prayers,” she tweeted.
BREAKING: El-Rufai tests positive for coronavirus
The governor, in a live broadcast said he submitted a sample for the COVID-19 test and the result came in positive.
He stated he has been in isolation according to doctors’ order.
He said: “Earlier this week, I submited a sample for the COVID-19 test and the result came in this evening and I regret to say that it is positive.
“According to the protocols for managing COVID-19, I am in self-isolation as required by the case management guidelines of the NCDC for a someone that is no showing symptoms.
“I wish to appeal to the people of Kaduna State to continue to closely observe the preventive measures already announced.
“It is most important that everybody should do their utmost to stay safe, stay home and stay alive.
“The Deputy Governor is chairing our COVID Taskforce and will continue to issue statements from time to time,” he said
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