The training ground of Arsenal football club have been 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,” said Spaniard Arteta, 37.
“I took the test after feeling poorly. 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”.
The club were due to face Brighton in the Premier League at Amex Stadium on Saturday (15:00 GMT) but Brighton released a statement, shortly after confirmation of Arteta’s positive test, announcing that the game had been called off.
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 the rest of this weekend’s scheduled fixtures.