Players and staff who had recent contact with Arteta will self-isolate and Arsenal have closed their training ground.
Brighton were set to face the Gunners at the Amex following a week that has witnessed leagues across Europe suspended or playing matches behind closed doors.
Arsenal already had players in self-isolation this week as a precaution following a recent meeting with Nottingham Forest and Olympiacos FC owner Evangelos Marinakis - who confirmed he tested positive for the virus earlier this week.
Arsenal managing director Vinai Venkatesham said their 37-year-old Spanish manager was "disappointed but in good spirits".
"The health of our people and the wider public is our priority and that is where our focus is," he added.
"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."
A statement from Premier League read: "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 UK government is considering banning UK sporting fixtures amid the outbreak but it will not happen immediately.