Arsenal have closed their training ground as a result of Arteta's positive test, with Gunners players and club staff who had recent contact with the Spaniard now forced to self-isolate.
"This is really disappointing but I took the test after feeling poorly," Arteta said in a statement on Arsenal's website.
"I will be at work as soon as I'm allowed."
Arsenal confirmed the shock news just minutes after the Premier League had said all fixtures would go ahead this weekend despite the spread of the global pandemic.
Arsenal, due to play at Brighton in the Premier League on Saturday, said it was "clear we will not be able to play some fixtures on their currently scheduled dates".
"Our London Colney training centre has been closed after head coach Mikel Arteta received a positive Covid-19 result this evening," the Arsenal statement said.
"Arsenal personnel who had recent close contact with Mikel will now self-isolate in line with Government health guidelines.
"We expect this to be a significant number of people from Colney, including the full first-team squad and coaching staff."
Arsenal are now trying to trace any other people who may have had contact with Arteta.
Arsenal managing director Vinai Venkatesham added: "The health of our people and the wider public is our priority and that is where our focus is.
"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."
The news of Arteta's positive test could force the Premier League to cancel English top-flight matches.
Arsenal's game at Manchester City last Wednesday had been called off after Nottingham Forest and Olympiakos owner Evangelos Marinakis announced on Tuesday that he had contracted the virus.
Marinakis met Arsenal staff and players during a Europa League tie at the Emirates Stadium on February 27.
"In light of Arsenal's announcement tonight confirming that their first-team coach Mikel Arteta has tested positive for COVID-19, the Premier League will convene an emergency club meeting tomorrow morning regarding future fixtures," the Premier League said.
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